Further information:
James C. Spall
Johns Hopkins University
Applied Physics Laboratory
11100 Johns Hopkins Rd.
Laurel, MD 207236099
USA

Abdulla, M.S. and Bhatnagar, S. (2007), 

"Parametrized ActorCritic Algorithms for FiniteHorizon MDPs,"
Proceedings of the American Control Conference, 1113 July 2007, New York City, USA, pp. 534–539 (paper WeA16.4) (presents two algorithms to compute optimal policies for finitehorizon Markov decision processes).
Top 

Abdulla, M.S. and Bhatnagar, S. (2007), 

“Reinforcement Learning Based Algorithms for Average Cost Markov Decision Processes,”
Discrete Event Dynamic Systems, vol. 17, pp. 23–52 (application of SPSA in actorcritic algorithms for solution of infinite horizon Markov decision processes).
Top 
Abdulsadda, A.T. and Iqbal, K. (2011), 

"An Improved SPSA Algorithm for System Identification Using Fuzzy Rules for Training Neural Networks,"
International Journal of Automation and Computing, vol. 8(3), pp. 333–339 (version of algorithm that entails fuzzy adaptive gain sequences, gradient smoothing, and a step rejection procedure to enhance convergence and stability).
Top 
Aboulaich, R., Ellaia R., and El Moumen S. (2010), 

"The MeanVarianceCVaR model for Portfolio Optimization Modeling using a MultiObjective Approach Based on a Hybrid Method,”
Mathematical Modelling of Natural Phenomena, vol. 5(7), pp. 103−108 (considers problem of portfolio selection, by using the normal boundary intersection approach based on a new hybrid algorithm of SPSA and simulated annealing).
Top 
Aksakalli, V. and Ursu, D. (2006), 

"Control of Nonlinear Stochastic Systems: ModelFree Controllers versus Linear Quadratic Regulators,"
Proceedings of the IEEE Conference on Decision and Control, 13–15 December 2006, San Diego, CA, USA, pp. 4145–4150 (paper ThIP8.3) (comparison of SPSAbased modelfree controller to linear quadratic regulators).
Top 
Alessandri, A., Bolla, R., Grassia, A.F., and Reppetto, M. (2006), 

"Identification of Freeway Macroscopic Models using Information from Mobile Phones,"
Proceedings of the American Control Conference, 14–16 June 2006, Minneapolis, MN, pp. 3801–3806 (paper ThC08.5) (parameter estimation for a freeway traffic flow model).
Top 
Alessandri,
A. and Parisini, T. (1997), 

"Nonlinear
Modelling of Complex LargeScale Plants Using Neural Networks and
Stochastic Approximation,"
IEEE Transactions on Systems, Man, and Cybernetics
—
A, vol. 27, pp. 750757
(model parameter estimation/fault detection).
Top 
Altaf, M.U., Heemink, A.W., Verlaan M., and Hoteit, I. (2011), 

"Simultaneous Perturbation Stochastic Approximation for Tidal Models,"
Ocean Dynamics, vol. 61(8), pp. 1093−1105 (automated calibration for tidal calibration of
Dutch continental shelf model, which is used to forecast storm surges in the North Sea).
Top 
Antal, C., Granichin, O., and Levi, S. (2010), 

"Adaptive Autonomous Soaring of Multiple UAVs using Simultaneous Perturbation Stochastic Approximation,"
Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, GA, 15−17 Dec. 2010, pp. 3656−3661 (algorithm for maximizing flight duration of a single UAV [Uninhabited Air Vehicle] and group of UAVs using thermal model developed at NASA−Dryden; SPSA used for detection of center of thermal updraft where vertical velocity of air stream is highest).
Top

Arahal, M.R., Cirre, C.M., and Berenguel, M. (2008), 

"Serial GreyBox Model of a Stratified Thermal Tank for Hierarchical Control of a Solar Plant,"
Solar Energy, vol. 82(5), pp. 441–451 (building model for control for existing small solar power system in Spain).
Top 
Balakrishna, R., Antoniou, C., BenAkiva, M., Koutsopoulos, H.N., and Wen, Y. (2007), 

"Calibration of Microscopic Traffic Simulation Models: Methods and Application,"
Transportation Research Record: Journal of the Transportation Research Board, no. 1999, pp. 198207
(largescale application to building traffic simulation, with emphasis on practical issues).
Top 
Balakrishna, R. and Koutsopoulos, H.N. (2008), 

"Incorporating WithinDay Transitions in the Simultaneous Offline Estimation of Dynamic OriginDestination Flows without Assignment Matrices,"
Transportation Research Record: Journal of the Transportation Research Board, no. 2085, pp. 31–38 (offline method for estimating dynamic origin−destination matrices without using assignment matrices).
Top 
Baltcheva, I., Cristea, S., VázquezAbad, F.J., and De Prada,
C. (2003), 

"Simultaneous
Perturbation Stochastic Approximation for Realtime Optimization
of Model Predictive Control,"
Proceedings of the First Industrial Simulation
Conference (ISC 2003), Valencia, Spain,
June 2003, pp. 533537
(global optimization for model predictive control).
Top 
Bangerth, W., Klie, H., Matossian, V., Parashar, M., Wheeler, M.F. (2006), 

"An Autonomic Reservoir Framework for the Stochastic Optimization of Well Placement,"
Cluster Computing, vol. 8(4), pp. 255–269 (use of SPSA with simulator for optimal placement of wells in oil and environmental applications).
Top 
Bartkute, V. and Sakalauskas, L. (2006), 

"Application of Stochastic Approximation in Technical Design,"
in Computer Aided Methods in Optimal Design and Operations (I. Bogle and J. Zilinskas, eds.), Series on Computers and Operations Research, vol. 7, World Scientific Publishers, Singapore, pp. 29–38 (development of termination rule based on best function values provided during optimization).
Top 
Bartkute, V. and Sakalauskas, L. (2007), 

"Simultaneous Perturbation Stochastic Approximation for Nonsmooth Functions,"
European Journal on Operational Research, vol. 181(3), pp. 1174–1188 (modification of SPSA to have convergence with nondifferentiable functions).
Top 
Bertsimas, D., Nohadani, O., and Teo, K.M. (2007), 

"Robust Optimization in Electromagnetic Scattering Problems,"
Journal of Applied Physics, vol. 101(7), article no. 074507 (comparison of gradientbased and gradientfree [SPSA] optimization for electromagnetic scattering problems with many degrees of freedom).
Top 

Bhatnagar, S. (2005), 

"Adaptive
Multivariate ThreeTimescale Stochastic Approximation Algorithms
for Simulation Based Optimization,"
ACM Transactions on Modeling and Computer Simulation, vol. 15,
pp. 74–107 (advanced methods for Hessian matrix estimation in the context of simulation optimization; applications in queuing networks).
Top

Bhatnagar, S. (2007), 

"Adaptive NewtonBased Multivariate Algorithms for Simulation Optimization,"
ACM Transactions on Modeling and Computer Simulation, vol. 18, pp. 2:1–2:35 (develops several convolutionbased [smoothed functional] methods for Hessian matrix estimation in the context of simulation optimization).
Top 
Bhatnagar, S. (2010), 

"An Actor–Critic Algorithm with Function Approximation for Discounted Cost Constrained Markov Decision Processes,"
Systems and Control Letters, vol. 59(12), pp. 760–766 (actor–critic reinforcement learning that incorporates a temporal difference critic; Markov decision process when the state and action spaces can be large).
Top 
Bhatnagar, S. (2011), 

“Simultaneous Perturbation and Finite Difference Methods,”
in Wiley Encyclopedia of Operations Research and Management Science (J. Cochran, ed.), vol. 7, pp. 4969−4991, Wiley, Hoboken, NJ (general review of SPSA and FDSA, including several extensions).
Top 
Bhatnagar, S. and Abdulla, M.S. (2006), 

"A Reinforcement Learning Based Algorithm for Finite Horizon Markov Decision Processes,"
Proceedings of the 45th IEEE Conference on Decision and Control, 13–15 December 2006, San Diego, CA, USA, pp. 5519–5524 (paper FrB09.1) (simulationbased algorithm for finitehorizon Markov decision processes with finite state and finite action space).
Top 
Bhatnagar, S. and Babu, K. (2008), 

"New Algorithms of the Qlearning Type,"
Automatica, vol. 44(4), pp. 11111119 (two algorithms for Qlearning that use the twotimescale stochastic approximation methodology; work covers areas of reinforcement learning and Markov decision processes).
Top 
Bhatnagar, S. and Borkar, V.S. (2003), 

"Multiscale
Chaotic SPSA and Smoothed Functional Algorithms For Simulation Optimization,"
Simulation, vol. 79, pp. 568580
(use of chaosbased generator for random perturbation sequences
in high dimensions).
Top 
Bhatnagar, S. and Kowshik, H.J. (2005), 

"A Discrete Parameter Stochastic Approximation Algorithm for Simulation Optimization,"
Simulation, vol. 81(11), pp. 757–772 (discrete parameter optimization with application to admission control in communication networks).
Top 
Bhatnagar, S. and Kumar, S. (2004), 

“A
Simultaneous Perturbation Stochastic ApproximationBased Actor—Critic
Algorithm for Markov Decision Processes,”
IEEE Transactions on Automatic Control, vol. 49, pp. 592–598
(alternative to dynamic programming for Markov decision processes).
Top

Bhatnagar, S. and Reddy, I. (2005), 

"Optimal
Threshold Policies for Admission Control in Communication Networks
via Discrete Parameter Stochastic Approximation,"
Telecommunications Systems, vol. 29,
pp. 9–31
(admission control of packets in communication networks).
Top

Bhatnagar,
S., Fu, M.C., and Marcus, S.I. (1999), 

"RateBased
ABR Flow Control Using Two Timescale SPSA,"
Proceedings of the SPIE
—
The International Society for Optical
Engineering, vol. 3841, pp.142149
(simulationbased optimization for networks).
Top

Bhatnagar,
S., Fu, M.C., and Marcus, S.I. and Bhatnagar, S. (2001), 

"Two
Timescale Algorithms for Simulation Optimization of Hidden Markov
Models,''
IIE Transactions, vol. 33, pp. 245258
(simulationbased optimization using two timescale SPSA).
Top

Bhatnagar,
S., Fu, M.C., and Marcus, S.I., and Fard, P.J. (2001), 

"Optimal
Structured Feedback Policies for ABR Flow Control Using Two Timescale
SPSA,''
IEEE/ACM Transactions on Networking, vol. 9, pp. 479491 (closedloop
feedback control in ATM networks).
Top

Bhatnagar, S., Fu, M.C., Marcus, S.I., and Wang, I.J. (2003),


"TwoTimescale
Simultaneous Perturbation Stochastic Approximation Using Deterministic
Perturbation Sequences,"
ACM Transactions on Modeling and Computer Simulation,
vol. 13, pp. 180209 (use of
deterministic—vs. random—perturbation vectors).
Top 
Boon, J. (2007), 

"Generating Exact DOptimal Designs for Polynomial Models,"
Proceedings of the Spring Simulation Multiconference, 25–29 March 2007, Norfolk, VA, USA, pp. 121–126 (comparison of SPSA, random search, and standard exchange algorithms for finding Doptimal experimental designs).
Top 
Brooks, O. (2007), 

"Solving Discrete Resource Allocation Problems using the Simultaneous Perturbation Stochastic Approximation (SPSA) Algorithm,"
Proceedings of the Spring Simulation Multiconference, 25–29 March 2007, Norfolk, VA, USA, pp. 55–62 (comparing the performance of stochastic optimization algorithms when applied to discrete resource allocation problems).
Top 
Burnett, R. (2004), 

“Application
of Stochastic Optimization to Collision Avoidance,”
Proceedings of the American Control Conference, 29 June–2
July 2004, Boston, MA, pp. 2789–2794
(comparison of random search, SPSA, and simulated annealing in
marine vessel traffic management).
Top

Cao, X. (2011), 

“Preliminary Results on NonBernoulli Distribution of Perturbations for Simultaneous Perturbation Stochastic Approximation,”
Proceedings of the American Control Conference, 29 June1 July 2011, San Francisco, CA, pp. 2669−2670 (paper ThB10.6) (considers use of one type of nonBernoulli distribution for the components of perturbation vector; distribution considered is “segmented uniform,” which meets theoretical conditions for perturbations).
Top 
Cauwenberghs,
G. (1994), 

"Analog
VLSI Autonomous Systems for Learning and Optimization,"
Ph.D. dissertation, California Institute of Technology
(issues in hardware implementation for neural networks).
Top

Cauwenberghs,
G. (1996), 

"An
Analog VLSI Recurrent Neural Network Learning a ContinuousTime
Trajectory,"
IEEE Transactions on Neural Networks, vol.
7, pp. 346361
(first demonstration of SPSA dynamic optimization on an analog VLSI
chip).
Top

Cauwenberghs,
G. (1997), 

"Analog
VLSI Stochastic Perturbative Learning Architectures,"
International Journal of Analog Integrated Circuits and Signal Processing,
vol. 13, pp. 195209
(extension of SPSA to reinforcement learning; VLSI implementation).
Top

Chan, B.L., Doucet, A., and Tadic, V.B. (2003), 

"Optimisation
of Particle Filters Using Simultaneous Perturbation Stochastic Approximation,"
Proceedings of IEEE International Conference
on Acoustics, Speech, and Signal Processing, April 2003, Hong Kong, vol. VI, pp. 681684
(optimization of particle filter methods, a.k.a. sequential Monte
Carlo methods).
Top 
Cheema, J.S., Sankpal, N.V., Tambe, S.S., and Kulkarni, B.D. (2002),


"Genetic
Programming Assisted Stochastic Optimization Strategies for Optimization
of Glucose to Gluconic Acid Fermentation,"
Biotechnolgy Progress, vol. 18, pp. 13561365
(optimization of inputs for genetic programming via SPSA).
Top 
Chen, H.F.,
Duncan, T.E., and PasikDuncan, B. (1996), 

"A
Stochastic Approximation Algorithm with Random Differences,"
Proceedings of the 13^{th} IFAC World
Congress, vol. H, 30 June5
July 1996, San Francisco, CA, pp. 493496
(alternative convergence conditions for SPSA).
Top 
Chien, S.I. and Luo, J. (2008), 

"Optimization of Dynamic Ramp Metering Control with Simultaneous Perturbation Stochastic Approximation,"
Control and Intelligent Systems, scheduled for fall 2008 issue (dynamic ramp metering traffic control to maximize the total throughput subject to the constraints of link densities, capacities, and metering rates).
Top 
Chin, D.C.
(1994), 

"A
More Efficient Global Optimization Algorithm Based on Styblinski
and Tang,"
Neural Networks, vol.
7, pp. 573574
(global optimization implementation).
Top

Chin, D.C.
(1996), 

"Efficient
Identification Procedure for Inversion Processing,"
Proceedings of the IEEE Conference on Decision
and Control, 1113
December 1996, Kobe, Japan, pp. 31293130
(nonlinear signal inversion). Top 
Chin, D.C.
(1997), 

"Comparative
Study of Stochastic Algorithms for System Optimization Based
on Gradient Approximations,"
IEEE Transactions on Systems, Man, and Cybernetics
— B, vol. 27, pp. 244249
(theoretical and numerical efficiency analysis).
Top

Chin,
D.C. (1999), 

"The
Simultaneous Perturbation Method for Processing Magnetospheric Images,"
Optical Engineering, vol. 38, pp. 606611
(a nonlinear regressiontype problem with comparisons to simulated
annealing).
Top

Chin,
D.C. and Smith, R.H. (1994), 

"A
Traffic Simulation for MidManhattan with ModelFree Adaptive Signal
Control,"
Proceedings of the Summer Computer Simulation
Conference, pp. 296301
(traffic control application).
Top

Chin,
D.C. and Srinivasan, R. (1997), 

"Electrical
Conductivity Object Locator: Location of Small Objects Buried at
Shallow Depths,"
Proceedings of the Unexploded Ordnance (UXO)
Conference, pp. 5057
(application with finiteelement models). Top 
Chin,
D.C., Srinivasan, R., and Ball, R.E. (1999), 

"Discrimination
of Buried Plastic and Metal Objects in Subsurface Soil,"
in Information Processing for Remote Sensing,
ed., C.H. Chen, World Scientific, New Jersey, pp. 565570
(application in mine detection).
Top

Chin,
D. C., Srinivasan, R., and Ball, R.E. (2001), 

"3D
Discrimination of Buried Object in Subsurface Soil via Magnetic
Sensors,"
Proceedings of the American Control Conference,
2527
June 2001, Arlington, VA, pp. 13691374
(inverse model estimation via twodimensional measurements).
Top

Chinthalapati, V.L.R. and Bhatnagar, S. (2006), 

"A Simultaneous Deterministic Perturbation ActorCritic Algorithm with an Application to Optimal Mortgage Refinancing,"
Proceedings of the 45th IEEE Conference on Decision and Control, 1315 December 2006, San Diego, CA, USA, pp. 4151–4156 (paper ThIP8.4) (SPSA with deterministic perturbations for enhanced performance with an application to a problem of mortgage refinancing).
Top 
Christensen, D.J., Sprowitz A., and Ijspeert A.J. (2010), 

“Distributed Online Learning of Central Pattern Generators in Modular Robots,”
From Animals to Animats 11 (S. Doncieux et al., eds), Lecture Notes in Artificial Intelligence, vol. 6226, pp. 402−412, Springer Berlin/Heidelberg (online learning of locomotion gaits for modular robots; considers effects of module failures, different robot morphologies, and rough terrains).
Top 
Cipriani, E. Florian, M., Mahut, M., and Nigro, M. (2011), 

“A Gradient Approximation Approach for Adjusting Temporal OriginDestination Matrices,”
Transportation Research, Part C—Emerging Technologies, vol. 19(2), pp. 270282 (method to solve for dynamic traffic demand matrix; solution produces acceptable computational times for offline applications and uses input traffic counts and speeds, prior origindemand matrices, and other aggregate demand data for inputs)
Top 
ColeRhodes, A., Johnson, K., and LeMoigne, J. (2002), 

"Multiresolution
Registration of RemoteSensing Images Using Stochastic Gradient,"
SPIE Aerosense 2002, Wavelet Applications
IX, vol. 4738, April 2002, Orlando, FL, pp. 4455
(image registration with waveletbased preprocessing).
Top

ColeRhodes, A., Johnson, K., LeMoigne, J., and Zavorin, I. (2003), 

"Multiresolution
Registration of Remote Sensing Imagery by Optimization of Mutual
Information Using a Stochastic Gradient,"
IEEE Transactions on Image Processing,
vol. 12, pp. 14951511 (image
registration based on correlation and mutual information).
Top 
Constantini, G. and Uncini, A. (2003), 

"RealTime
Room Acoustic Response Simulation by an IIR Adaptive Filter,"
Electronics Letters, vol. 39, pp. 330332
(signal processing application in music).
Top

Cupertino, F., Mininno, E., Naso, D., and Salvatore, L. (2007), 

"A Comparison of SPSA method and Compact Genetic Algorithm for the Optimization of Induction Motor Position Control,"
Proceedings of the European Conference on Power Electronics and Applications, 2–5 September 2007, pp. 1–10 (implementation of selfoptimizing embedded control schemes for induction motor drives).
Top

Cupertino, F., Mininno, E., Naso, D., and Turchiano, B. (2006), 

"An Experimental Implementation of SPSA Algorithms for Induction Motor Adaptive Control,"
Proceedings of SMCals/06, 2006 IEEE Mountain Workshop on Adaptive and Learning Systems, 24–26 July 2006, Utah State University, Logan, U.S.A., pp. 66–71 (implementation of several versions of SPSA for embedded control).
Top 
Dabbene, F., Gay, P., and Sacco N. (2008), 

"Optimisation of FreshFood Supply Chains in Uncertain Environments, Part I: Background and Methodology,"
Biosystems Engineering, vol. 99(3), pp. 348–359 (optimization of food supply chains that manages the tradeoff between logistical costs and some indices measuring the quality of the food as perceived by the consumer).
Top 
Das, S., Spall, J.C., and Ghanem, R. (2010), 

“Efficient Monte Carlo Computation of Fisher Information Matrix Using Prior Information,”
Computational Statistics and Data Analysis, vol. 54(2), pp. 272–289 (considers simultaneous perturbation gradient approximation in a Monte Carlo method for estimating Fisher information matrix in complex statistical models; extends Spall (2005) method to exploits partial knowledge of form of information matrix).
Top 
De Craene, M.S., Macq, B., Marques, F., Salembier, P., and Warfield, S.K. (2008), 

"Unbiased GroupWise Alignment by Iterative Central Tendency Estimation,"
Mathematical Modelling of Natural Phenomena, vol. 3(6), pp. 2−32 (joint alignment of a large collection of segmented images into the same system of coordinates; expectationmaximization [EM] estimation used for hidden variables).
Top 
Dippon,
J. and Renz, J. (1994), 

"Weighted
Means of Processes in Stochastic Approximation,"
Universitat Stuttgart, Mathematisches Institut A,
Preprint 945
(evaluation of PolyakRuppert iterate averaging for SPSA).
Top
. 
Dippon,
J. and Renz, J. (1997), 

"Weighted
Means in Stochastic Approximation of Minima,"
SIAM Journal of Control and Optimization,
vol. 35, pp. 18111827
(iterate averaging and optimal rates Top 
Dong, N. and Chen, Z. (2012), 

“A Novel Data Based Control Method Based Upon Neural Network and Simultaneous Perturbation Stochastic Approximation,”
Nonlinear Dynamics, vol. 67(2), pp. 957–963 (modification of modelfree control method to have loss that minimizes both the output error and its rate of change, with the aim of yielding a smoother system output).
of convergence).
Top 
El Moumen, S., Ellaia, R., and Aboulaich, R. (2011), 

“A New Hybrid Method for Solving Global Optimization Problem,”
Applied Mathematics and Computation, vol. 218(7), pp. 3265−3276 (presents hybrid method that finds a local minimum using descent method based on SPSA, followed by simulated annealing to escape from current local minimum; process is repeated until convergence).
Top 
Fedin, D.S., Granichin, O.N., Dedkov, Yu.S., and Molodtsov, S.L. (2008), 

"Method of Measurements with Random Perturbation: Application in Photoemission Experiments,"
Review of Scientific Instruments, vol. 79(3), paper no. 036103 (application to filtering systematic noise with nonzero mean value in photoemission data; used a series of 50 singlescan photoemission spectra).
Top 
Finck, S. and Beyer, H.G. (2012), 

“Performance Analysis of the Simultaneous Perturbation Stochastic Approximation Algorithm on the Noisy Sphere Model,”
Theoretical Computer Science, vol. 419, pp. 50–72 (theoretical comparison of different algorithms with spherical loss function; method allows for convergence results for nonnoisy and noisy optimization to be obtained simultaneously; includes comparison of SPSA and evolution strategies).
Top 
Flaxman, A., Kalai, A.T., and McMahan, H.B. (2005),


“Online
Convex Optimization in the Bandit Setting: Gradient Descent Without
a Gradient,”
Proceedings of the 16th Symposium on Discrete Algorithms (SODA),
Vancouver, Canada, pp. 385–394
(distributionfree analysis with very few assumptions).
Top

Fu,
M.C. and Hill, S.D. (1997), 

"Optimization
of Discrete Event Systems via Simultaneous Perturbation Stochastic
Approximation,"
Transactions of the Institute of Industrial Engineers,
vol.
29, pp. 233243
(simulationbased optimization for discreteevent and queueing networks).
Top

Garrett, J. (2004), 

"Jointly
Optimizing Model Complexity and DataProcessing Parameters with
MixedInput SPSA,"
36th Symposium on the Interface: Computing Science and Statistics,
26–29
May 2004, Baltimore, MD (optimization in predictive modeling and
classification of featureselection and modelcomplexity parameters).
Top

Gerencsér,
L. (1997), 

"Rate
of Convergence of Moments of Spall's SPSA Method,"
in Stochastic Differential and Difference Equations
(Csiszár and Gy. Michaletzky, eds.),
Series on Progress in Systems and Control Theory, vol. 23, Birkhäuser,
Boston, pp. 6775
(convergence conditions for means and other moments of SPSA
iterate).
Top

Gerencsér, L.
(1999), 

"Convergence
Rate of Moments in Stochastic Approximation with Simultaneous Perturbation
Gradient Approximation and Resetting,"
IEEE Transactions on Automatic Control,
vol. 44, pp. 894905
(convergence conditions for moments of SPSA iterate).
Top 
Gerencsér, L.
and Vágó, Z. (1999), 

"Stochastic
Approximation for Function Minimization Under Quantization Error,"
Proceedings of the IEEE Conference on Decision
and Control, 710
December 1999, Phoenix, AZ, pp. 23732376
(convergence analysis for optimization problems with nonrandom
noise).
Top

Gerencsér, L.
and Vágó, Z. (2000), 

"SPSA
in NoiseFree Optimization,"
Proceedings of the American Control Conference,
2830
June 2000, Chicago, IL, pp. 32843288 (theoretical
analysis of convergence rate when loss measurements are noisefree).
Top

Gerencsér, L.
and Vágó, Z. (2001), 

"The
Mathematics of NoiseFree SPSA,"
Proceedings of the IEEE Conference on Decision
and Control, 47
December 2001, Orlando, FL, pp. 44004405
(analysis of convergence rate with noisefree loss measurements).
Top

Gerencsér, L.,
Hill, S.D., Vágó, Z. (1999), 

"Optimization
over Discrete Sets via SPSA,"
Proceedings of the IEEE Conference on Decision
and Control, 710
December 1999, Phoenix, AZ, pp. 17911795
(use of SPSA for discrete optimization).
Top 
Gerencsér, L.,
Hill, S.D., and Vágó,
Z. (2001), 

"Discrete
Optimization via SPSA,"
Proceedings of the American Control Conference,
2527 June 2001, Arlington, VA, pp. 15031504 (SPSA for discrete
optimization, including new rate of convergence result).
Top 
Gerencsér, L.,
Hill, S.D., and Vágó,
Z. (2002), 

"Discrete
Optimization, SPSA, and Markov Chain Monte Carlo,"
Proceedings of the IEEE Conference on Decision
and Control, December 2002, Las Vegas, NV, pp. 23462347
(use of MCMC methods with SPSA).
Top 
Gerencsér, L., Hill, S.D., Vágó,
Z., and Vincze, Z. (2004), 

"Discrete
Optimization, SPSA, and Markov Chain Monte Carlo Methods,"
Proceedings of the American Control Conference,
29 June–2
July 2004, Boston, MA, pp. 3814–3819
(minimization of discrete convex functions and connection to MCMC).
Top

Gerencsér, L.,
Kozmann, G., and Vágó, Z. (1998), 

"SPSA
for NonSmooth Optimization with Application in ECG Analysis,"
Proceedings of the IEEE Conference on Decision
and Control, 1618
December 1998, Tampa, FL., pp. 39073908
(application in a classification problem).
Top

Gerencsér, L., Kozmann,
G., Vágó, Z., and Haraszti, K. (2002), 

"The
Use of the SPSA Method in ECG Analysis,”
IEEE Transactions on Biomedical Engineering,
vol. 49, pp. 10941101 (application
in biomedical classification problem). Top 
Gosavi,
A. (2002), 

"The
Effect of Noise on Artificial Intelligence and MetaHeuristic Techniques,”
Proceedings of the Artificial Neural Networks
in Engineering Conference (Intelligent Engineering Systems
Through Artificial Neural Networks), American Society of Mechanical
Engineering Press, vol. 12, pp. 981988
(effect of simulationbased noise on simulated annealing and SPSA).
Top 
Gosavi,
A. (2003), 

SimulationBased
Optimization: Parametric Optimization Techniques and Reinforcement
Learning,
Kluwer Academic, Boston (book including significant
discussion of SPSA in simulationbased optimization, especially
in Sects. 7.2.1 and 12.4.3). Top

Gosavi, A., Ozkaya, E., and Kahraman, A. (2007), 

"Simulation Optimization for Revenue Management of Airlines with Cancellations and Overbooking,"
OR Spectrum (special issue on revenue management), vol. 29, pp. 2138 (simulationbased solution to the seat allocation problem in the airline industry).
Top 
Graf, M. and Kimms, A. (2011), 

“An OptionBased Revenue Management Procedure for Strategic Airline Alliances,”
European Journal of Operational Research, vol. 215(2), pp. 459−469 (simulationbased optimization of airline capacity control process: whether to accept an incoming customer request for a seat or reject it in hope that another customer will request the seat later at a higher price).
Top 
Granichin,
O.N. (2002), 

"Randomized
Algorithms for Stochastic Approximation Under Arbitrary Disturbances,"
Automation
and Remote Control, vol. 63, pp. 209219 (handles
general noise distributions, with connections to quantum computing).
Top 
Granichin,
O.N. (2003), 

"Optimal
Convergence Rate of the Randomized Algorithms of Stochastic Approximation
in Arbitrary Noise,"
Automation
and Remote Control, vol. 64, pp. 252262
(optimization of algorithm parameters with dependence on distribution
of the simultaneous perturbation and smoothness of loss function).
Top 
Granichin, O., Gurevich, L., and Vakhitov, A. (2009), 

“SPSA with a Fixed Gain for Intelligent Control in Tracking Applications,”
Proceedings of the IEEE International Conference on Control Applications, 8−10 July 2009, St. Petersburg, Russia, pp. 1415−1420 (fixed gain SPSA is considered for problem of tracking a changing minimum point; paper establishes an upper bound to mean square estimation error in case of once differentiable loss and almost arbitrary noises).
Top 
Granichin, O.N. and Izmakova, O.A. (2005), 

"A Randomized Stochastic Approximation Algorithm for SelfLearning,"
Automation and Remote Control, vol. 66(8), pp. 12391248 (SPSAbased selflearning [unsupervised] algorithms).
Top 
Granichin
O.N. and Polyak, B.T. (2003), 

Randomized
Algorithms of Estimation and Optimization Under Almost Arbitrary
Noises,
Nauka, Moscow, Russia (English language contents for a book
in Russian; thorough treatment of SPSA and related algorithms under
general noise conditions). 
Granichin, O.N. and Vakhitov, A.T. (2006), 

"Accuracy for the SPSA Algorithm with Two Measurements,"
WSEAS Transactions on Systems, vol. 5(5), pp. 953957 (proves that moments of degree from 1 to 2 for the estimates are convergent).
Top 
Grigaitis D., Bartkute V., and Sakalauskas L. (2007), 

"An Optimization of System for Automatic Recognition of Ischemic Stroke Areas in Computed Tomography Images,"
Informatica, vol. 18(4), pp. 603614 (application to automatic recognition of ischemic stroke area on computed tomography [CT] images).
Top 
Grote, D.P., Henestroza, E., and Kwan, J.W. (2003), 

"Design
and Simulation of a Multibeamlet Injector for a High Current Accelerator,"
Physical Review Special Topics—Accelerators and
Beams, vol. 6, pp.
1420211420212
(optimal design for parts of a particle accelerator).
Top 
Gu, W.F., Xiang, C., Venkatesh, Y.V., Huang, D., and Lin, H. (2012), 

"Facial Expression Recognition using Radial Encoding of Local Gabor Features and Classifier Synthesis,"
Pattern Recognition, vol. 45(1), pp. 80−91 (SPSA used for estimating parameters in model new facial expression recognition scheme that is motivated by some characteristics of the human visual cortex).
Top 
Guo, C., Song, Q., and Cai, W. (2007), 

"A Neural Network Assisted Cascade Control System for Air Handling Unit,"
IEEE Transactions on Industrial Electronics, vol. 54(1), pp. 620628 (implementation in control for a heating, ventilating and airconditioning system, and comparison with traditional proportionalintegralderivative [PID] controllers).
Top 
Güven, T., La, R.J., Shayman, M.A., and Bhattacharjee, B. (2006), 

"MeasurementBased Optimal Routing on Overlay Architectures for Unicast Sessions,"
Computer Networks, vol. 50(12), pp. 1938–1951 (routing algorithm for loadbalance of intradomain traffic along multiple paths for multiple unicast sources; comparison with existing MATE routing algorithm).
Top 
Hahn, B. and Oldham, K. R. (2010), 

"A ModelFree OnOff Iterative Adaptive Controller Based on Stochastic Approximation,"
Proceedings of the American Control Conference, 30 June−2 July 2010, Baltimore, MD, USA, pp. 1665−1670 (paper WeC03.2) (adaptive controller applicable to servo systems performing repeated motions under strict power constraints).
Top 
Hao, L. and Yao, M. (2011), 

"SPSAbased step tracking algorithm for mobile DBS reception,"
Simulation Modelling Practice and Theory, vol. 19(2), pp. 837–846 (step tracking algorithm for Kuband mobile satellite communication used in mobile direct broadcasting satellite [DBS] reception).
Top 
He, Y., Fu, M.C, and Marcus, S.I. (2003), 

"Convergence
of Simultaneous Perturbation Stochastic Approximation for Nondifferentiable
Optimization,"
IEEE
Transactions on Automatic Control, vol. 48, pp. 14591463
(considers convergence for continuous but nondifferentiable functions).
Top

Heydon, B.D. and Hill, S.D. (2003), 

"Maximizing Target Damage Through Optimal Aimpoint Patterning,"
AIAA 3rd Biennial National Forum on Weapon System Effectiveness, 1820 November 2003, Seal Beach, CA (simulationbased optimization to aid in targeting and minimizing collateral damage) (distribution restricted to U.S. government agencies and their contractors).
Top 
Hill, S.D. (2005), 

“Discrete
Stochastic Approximation with Application to Resource Allocation,”
Johns Hopkins APL Technical Digest, vol. 26, pp. 15–21
(application to discrete optimization with discussion of resource
allocation problem).
Top

Hill,
S.D. and Fu, M.C. (1995), 

"Transfer
Optimization via Simultaneous Perturbation Stochastic Approximation,"
Proceedings of the Winter Simulation Conference,
eds. C. Alexopoulos, K. Kang, W.R. Lilegdon, and D. Goldsman, pp.
242249
(transit systems and queuing networks).
Top

Hill, S.D., Gerencsér, L., and Vágó,
Z. (2003), 

"Stochastic
Approximation on Discrete Sets Using Simultaneous Perturbation Difference
Approximations,"
Proceedings of the 37th Conference on Information Science and Systems,
1214 March 2003, The Johns Hopkins
University, CDROM Paper #17 (discrete optimization method).
Top 
Hill, S.D., Gerencsér, L., and Vágó,
Z. (2004), 

“Stochastic
Approximation on Discrete Sets Using Simultaneous Difference Approximations,”
Proceedings of the American Control Conference,
29 June–2
July 2004, Boston, MA, pp. 2795–2798
(discrete minimization, including some convergence theory).
Top

Hirokami, T., Maeda, Y., and Tsukada, H. (2006), 

"Estimation using Simultaneous Perturbation Stochastic Approximation,"
Electrical Engineering in Japan, vol. 154(2), pp. 30–39 (parameter estimation, including a convergence theorem and simulation study).
Top 
Hong, Y.Y., Chang, H.L., and Chiu, C.S. (2010), 

"HourAhead Wind Power and Speed Forecasting using Simultaneous Perturbation Stochastic Approximation (SPSA) Algorithm and Neural Network with Fuzzy Inputs,"
Energy, vol. 35(9), pp. 3870−3876 (proposes method of wind power and speed forecasting using a multilayer feedforward neural network with SPSAbased training; real wind power generation and wind speed data measured at a wind farm are used for simulation).
Top 
Hopkins,
H.S. (1997), 

"Experimental
Measurement of a 4D Phase Space Map of a Heavy Ion Beam,"
Ph.D. thesis, Dept. of Nuclear Engineering, University
of CaliforniaBerkeley,
December 1997 (control to reduce alignment errors in targeting
of ion beam).
Top

Hu, J., Zhu, W., Su, Y., and Wong, W. K. (2010), 

"Controlled Optimal Design Program for the Logit Dose Response Model,"
Journal of Statistical Software, vol. 35(6), pp. 1−17 (generating controlled Doptimal and other designs for doseresponse studies, which can incorporate prior information and multiple objectives; combined with crossentropy method for optimization).
Top 
Hutchison, D.W. (2002), 

"On
an Efficient Distribution of Perturbations for Simulation Optimization
Using Simultaneous Perturbation Stochastic Approximation,"
Proceedings of the IASTED International Conference on Applied Modelling
and Simulation, 46 November
2002, Cambridge, MA, pp. 440445
(careful empirical evaluation of Bernoulli and nonBernoulli perturbation
distributions).
Top 
Hutchison,
D.W. and Hill, S.D. (2000), 

"Simulation
Optimization of Airline Delay Using Simultaneous Perturbation Stochastic
Optimization,"
Proceedings of the 33rd Annual Simulation Symposium,
1620
April 2000, Washington, DC, pp. 253258
(application in simulationbased optimization).
Top

Hutchison,
D.W. and Hill, S.D. (2001), 

"Simulation
Optimization of Airline Delay with Constraints,"
Proceedings of the 2001 Winter Simulation Conference,
912
December 2001, Arlington, VA, pp. 10171022
(resource allocation in airline networks).
Top

Ji,
X.D. and Familoni, B.D. (1996), 

"Experimental
Study of Direct Adaptive SPSA Control System with Diagonal Recurrent
Neural Network Controller,"
Proceedings of the IEEE SoutheastCon '96,
pp. 525528
(evaluation with recurrent neural networks).
Top

Ji,
X.D. and Familoni, B.D. (1999), 

"A
Diagonal Recurrent Neural NetworkBased Hybrid Direct Adaptive SPSA
Control System,"
IEEE Transactions on Automatic Control,
vol. 44, pp. 14691473
(a hybrid SPSA/PID adaptive controller with a recurrent neural network
as function approximator).
Top 
Johannsen,
D.A., Wegman, E.J., Solka, J.L., and Priebe, C.E. (2004), 

"Simultaneous
Selection of Features and Metric for Optimal Nearest Neighbor Classification,"
Communications in Statistics–Theory and Methods, vol. 33, pp. 21372157 (pattern
recognition application).
Top 
Kiranyaz, S., Ince, T., and Gabbouj, M. (2011), 

"Stochastic Approximation Driven Particle Swarm Optimization with Simultaneous Perturbation—Who will Guide the Guide?,"
Applied Soft Computing, vol. 11(2), pp. 2334−2347 (SPSA used to guide particle swarm optimization [PSO], with finding that even if SPSA parameters are not tuned well, results of SAdriven PSO are still better than the best of PSO alone).
Top 
Kizito, R., Roggemann, M.C., Schulz, T.J., and Zhang,
Y. (2004), 

"Image
Sharpness MetricBased Deformable Mirror Control for Beam Projection
Systems Operating in Strong Scintillation,"
Proceedings of the SPIE—The International Society for Optical
Engineering, vol. 5160, pp. 406–416 (controlling
a deformable mirror in beam projection systems).
Top

Kleinman,
N.L. (1996), 

"Stochastic
Approximation Algorithms: Theory and Applications,"
Ph.D. thesis, Dept. of Mathematical Sciences (now Dept. of Applied Mathematics and Statistics), The
Johns Hopkins University (use of SPSA in simulationbased optimization
and BerryEsseentype rates of convergence to normality).
Top

Kleinman,
N.L., Hill, S.D., and Ilenda, V.A. (1997), 

"SPSA/SIMMOD
Optimization of Air Traffic Delay Cost,"
Proceedings of the American Control Conference,
46
June 1997, Albuquerque, NM, pp. 11211125
(applications to air traffic network). Top 
Kleinman,
N.L., Spall, J.C., and Naiman, D.Q. (1999), 

"SimulationBased
Optimization with Stochastic Approximation Using Common Random
Numbers,"
Management Science,
vol. 45, pp. 15701578
(evaluation of SPSA and finitedifference methods in simulationbased
optimization when common random numbers are feasible).
Top 
Klie, H., Bangerth, W., Wheeler, M., Parashar, M.,
and Matossian, V. (2004), 

“Parallel
Well Location Optimization Using Stochastic Algorithms on the
Grid Computational Framework,”
Proceedings of the 9th European Conference on the Mathematics
of Oil Recovery (ECMOR IX), CDROM (optimizing oil well locations
using SPSA).
Top

Koch, M.I., Chin, D.C.,
and Smith, R.H. (1997), 

"NetworkWide
Approach to Optimal Signal Light Timing for Integrated Transit Vehicle
and Traffic Operations,"
Proceedings of the 7^{th} National Conference
on Light Rail Transit, vol. 2, National
Academy of Sciences Press, pp. 126131
(control of traffic and transit vehicles at a networkwide level).
Top 
Kocsis, L., Szepesvári, Cs. and Winands, M.H.M.
(2005), 

"RSPSA:
Enhanced Parameter Optimisation in Games,"
Proceedings of the 11th Advances in Computer
Games Conference (ACG11), 6–8 September 2005, Taipei, Taiwan (optimizing
parameters of game programs: poker, lines of actions; uses common
random numbers and antithetic random numbers).
Top

Kocsis, L. and Szepesvári, C. (2006), 

"Universal Parameter Optimisation in Games Based on SPSA,"
Machine Learning, vol. 63(3), pp. 249–286 (tuning of the large number of parameters that are crucial for the performance of automated gameplaying algorithms).
Top 
Kong, X., Yang, Y., Chen, X., Shao, Z., and Gao, F. (2011), 

“Quality Control via ModelFree Optimization for a Type of Batch Process with a Short Cycle Time and Low Operational Cost,”
Industrial and Engineering Chemistry Research, vol. 50(5), pp. 2994–3003 (modelfree optimization method for a batch process with short cycle time and low operational cost is proposed to improve the efficiency of quality control; demonstration on quality control of injection molding process)
Top 
Kothandaraman, G. and Rotea, M.A. (2003), 

"SPSA
Algorithm for Parachute Parameter Estimation,"
AIAA Paper No. 2003–2118,
17th AIAA Aerodynamic Decelerator Systems Technology Conference
and Seminar, Monterey, CA, May 2003, pp. 138–148
(parameter estimation for sixdegreeoffreedom parachute model).
Top

Kothandaraman, G. and Rotea, M.A. (2005), 

"SPSA Algorithm for Parachute Parameter Estimation,"
Journal of Aircraft, vol. 42(5), pp. 1229–1235 (algorithm to estimate unknown parameters of parachute models from flighttest data without use of analytical gradients; algorithm is used to estimate aerodynamic and apparent mass coefficients in model).
Top 
Lambert, P. and Banchs, R.E. (2007), 

"SPSA vs Simplex in Statistical Machine Translation Optimization,"
PAMM − Proc. Appl. Math. Mech., vol. 7(1), pp. 1062503–1062504 (comparison using IWSLT 2005 ChineseEnglish data; both methods showed similar performance, but SPSA was more robust to the choice of initial settings).
Top 
Lambert, P., Banchs, R.E., and Crego, J.M. (2007), 

"Discriminative Alignment Training without Annotated Data for Machine Translation,"
Proceedings Human Language Technologies 2007: The Conference of the North American Chapter of the Association for Computational Linguistics, Companion Volume, Short Papers, April 2007, Rochester, NY, USA, pp. 85–88 (machine learning application in the area of translations).
Top 
Lee, J.B. and Ozbay, K. (2008), 

"Calibration of a Macroscopic Traffic Simulation Model Using Enhanced Simultaneous Perturbation Stochastic Approximation Methodology,"
Transportation Research Board Annual Meeting paper no. 082964 (parameter estimation for traffic simulation based on a Bayesian sampling approach; includes example calibration for a portion of I880 in California).
Top 
Luman,
R.R. (1997), 

"Quantitative
Decision Support for Upgrading Complex Systems of Systems,"
Ph.D. thesis, School of Engineering and Applied
Science, George Washington University (use of first and secondorder
SPSA in simulationbased optimization).
Top

Luman,
R.R. (2000), 

"Upgrading
Complex Systems of Systems: A CAIV Methodology for Warfare Area
Requirements Allocation,"
Military Operations Research,
vol. 5(2), pp. 5375
(use of first and secondorder SPSA in simulationbased optimization).
Top 
Ma, J., Nie, Y., and Zhang, H.M. (2007), 

"Solving the Integrated Corridor Control Problem Using Simultaneous Perturbation Stochastic Approximation,"
Transportation Research Board Annual Meeting, Paper #071065 (control of traffic in a transportation corridor using traffic signal timing and ramp metering).
Top 
Ma, J., Dong, H., and Zhang, H.M. (2007), 

"Calibration of Micro Simulation with Heuristic Optimization Methods,"
Transportation Research Board Annual Meeting, Paper #071282 (estimation of microscopic traffic simulation; includes comparisons with genetic algorithm and trialanderror iterative adjustment).
Top 
Ma, J., Dong, H., and Zhang, H.M. (2007), 

"Calibration of Micro Simulation with Heuristic Optimization Methods,"
Transportation Research Record: Journal of the Transportation Research Board, vol. 1999, pp. 208217 (slightly updated version of TRB meeting paper above: estimation of microscopic traffic simulation; includes comparisons with genetic algorithm and trialanderror iterative adjustment).
Top 
Madan, D.B. (2010), 

"Variance Swap Portfolio Theory,"
Contemporary Quantitative Finance (C. Chiarella and A. Novikov, eds.), Springer Berlin Heidelberg, pp. 183194 (optimal portfolios of variance swaps are constructed taking account of both autocorrelation and cross asset dependencies).
http://dx.doi.org/10.1007/9783642034794_10
Top 
Maeda,
Y. (1996), 

"Time
Difference Simultaneous Perturbation Method,"
Electronics Letters,
vol. 32, pp. 10161018
(method for coping with nonstationarities in dynamic estimation).
Top 
Maeda,
Y. (2002), 

"RealTime
Control and Learning Using NeuroController via Simultaneous Perturbation
for Flexible Arm System,"
Proceedings of the American Control Conference, 810
May 2002, Anchorage, AK, pp. 25832588
(applications for robot arm control). Top 
Maeda,
Y. and Kanata, Y. (1994), 

"Extended
Adaptive RobbinsMonro Procedure Using Simultaneous Perturbation
for a LeastSquare Approximation Problem,"
Proceedings of the Asian Control Conference,
pp. 383386
(recursive estimation of inputoutput relationship by least squares).
Top

Maeda, Y. and Maruyama, T. (2003), 

"Natural
Gradient Using Simultaneous Perturbation Without Probability Densities
for Blind Source Separation,"
Proceedings of the 4th International Symposium on Independent Component
Analysis and Blind Signal Separation, Nara, Japan, April 2003,
pp. 439443 (natural gradient
method for blind source separation in signal processing).
Top 
Maeda, Y. and Toshiki, T. (2003), 

"FPGA
Implementation of a Pulse Density Neural Network With Learning Ability
Using Simultaneous Perturbation,"
IEEE Transactions on Neural Networks,
vol. 14, pp. 688695 (hardware
implementation of a pulse neural network).
Top 
Maeda,
Y. and Tsushio, K. (2002), 

"Blind
Signal Separation via Simultaneous Perturbation Method,"
Proceedings of the International Joint Conference
on Neural Networks, Honolulu, HI, 1217
May 2002 (method for extracting signals of interest from mixtures
of signals).
Top

Maeda, Y. and Wakamura, M. (2005), 

"Simultaneous Perturbation Learning Rule for Recurrent Neural Networks and Its FPGA Implementation,"
IEEE Transactions on Neural Networks, vol. 16(6), pp. 1664–1672 (hardware implementation in fieldprogrammable gate array [FPGA]).
Top 
Maeda
Y. and Yoshida T. (1999), 

"An
Active Noise Control Without Estimation of SecondaryPathANC Using
Simultaneous Perturbation,"
Proceedings of the International Symposium on
Active Control of Sound and Vibration (ACTIVE '99),
24
December 1999, Ft. Lauderdale, FL, pp. 985994
(active noise control scheme).
Top

Maeda,
Y., Hirano, H., and Kanata, Y. (1995), 

"A
Learning Rule of Neural Networks via Simultaneous Perturbation
and its Hardware Implementation,"
Neural Networks, vol.
8, pp. 251259
(pattern recognition).
Top

Maeda,
Y. and De Figueiredo, R.J.P. (1997), 

"Learning
Rules for NeuroController via Simultaneous Perturbation,"
IEEE Transactions on Neural Networks,
vol. 8, pp. 11191130
(use in neural networkbased control with applications in robotics).
Top

Maeda,
Y., Nakazawa, A., and Yakichi, K. (1999), 

"Hardware
Implementation of a Pulse Density Neural Network Using Simultaneous
Perturbation Learning Rule,"
Analog Intergrated Circuits and Signal Processing,
vol. 18, pp. 153162
(neural network training via circuit design with gate operations).
Top

Martin, S., Morison, G., Nailon, W., and Durrani,
T. (2004), 

“Fast
and Accurate Image Registration Using Tsallis Entropy and Simultaneous
Perturbation Stochastic Approximation,”
Electronics Letters, vol. 40, pp. 595–597
(Tsallis measure of mutual information is combined with SPSA to
register images).
Top

Martinez, J., Sawut, U., and Nakano, K. (2008), 

"Application of Nonlinear Observer with Simultaneous Perturbation Stochastic Approximation Method to Single Flexible Link SMC,"
Proceedings of SICE 2008—47th Annual Conference of the Society of Instrument and Control Engineers of Japan, Tokyo, Japan, 20−22 August 2008, pp. 2150−2155 vibration control of a onelink flexible arm system; involves parameter estimation for nonlinear observer).
Top 
Maryak,
J.L. (1997), 

"Some
Guidelines for Using Iterate Averaging in Stochastic Approximation,"
Proceedings of the IEEE Conference on Decision
and Control, 1012
December 1997, San Diego, CA, pp. 22872290
(exploration of iterate averaging for SPSA). Top 
Maryak, J.L., and Chin, D.C. (2001), 

"Global
Random Optimization by Simultaneous Perturbation Stochastic Approximation,"
Proceedings of the American Control Conference,
2527
June 2001, Arlington, VA, pp. 756762
(discusses use of SPSA for global search with and without the use of
additional injected noise).
Top

Maryak, J.L., and Chin, D.C. (2008), 

"Global Random Optimization by Simultaneous Perturbation Stochastic Approximation,"
IEEE Transactions on Automatic Control, vol. 53, pp. 780783 (updated version of above ACC 2001 paper on SPSA for global search with and without the use of additional injected noise).
Top 
Maryak,
J.L. and Spall, J.C. (2005), 

"Simultaneous
Perturbation Optimization for Efficient Image Restoration,"
IEEE Transactions on Aerospace and Electronic
Systems, vol. 41, pp. 356361
(application in recovering
an image from a degraded version of image).
Top

Maryak,
J.L., Smith, R.H., and Winslow, R.L. (1998), 

"Modeling
Cardiac Ion Channel Conductivity: Model Fitting Via Simulation,"
Proceedings of the Winter Simulation Conference
(D.J. Medeiros and E.F. Watson, eds.), pp.
15871590
(biomedical application involving model fitting; includes comparison
with simulated annealing).
Top 
McClary, D.W., Syrotiuk, V.R., and Kulahci M (2010), 

"SteepestAscent Constrained Simultaneous Perturbation for Multiobjective Optimization,"
ACM Transactions on Modeling and Computer Simulation, vol. 21(1), pp. 2:1−2:22 (considers simultaneous optimization of multiple responses in a dynamic system; example in crosslayer optimization of throughput, packet loss, and endtoend delay in a a selforganizing wireless network).
Top 
Merhof, D., Soza, G., Stadlbauer, A., Greiner, G., and Nimsky, C. (2007), 

"Correction of Susceptibility Artifacts in Diffusion Tensor Data Using NonLinear Registration,"
Medical Image Analysis, vol. 11(6), pp. 588603 (surgical application in image registration to localize major white matter tracts within the human brain; aim to achieve an optimal resection while avoiding postoperative neurological deficits).
Top 
Miranda, A.K. and Castillo, E.D. (2011), 

"Robust Parameter Design Optimization of Simulation experiments using Stochastic Perturbation Methods,"
Journal of the Operational Research Society, vol. 62, pp. 198–205 (considers SPSA for robust parameter design problems, with two example applications: a singlestage inventory system for which the quality of the solutions was easy to verify, and a more realistic manufacturing system). Top 
Mishra, V., Bhatnagar, S., and Hemachandra, N. (2007), 

"Discrete Parameter Simulation Optimization Algorithms with Applications to Admission Control with Dependent Service Times,"
Proceedings of the 46th IEEE Conference on Decision and Control, 1214 December 2007, New Orleans, LA, USA, pp. 29862991 (paper ThPI25.4) (comparisons with smoothed functional technique in particular queuing problem with discrete parameter space).
Top 
Mohamed, W. and Ben Hamza, A.B. (2010), 

"Medical Image Registration Using Stochastic Optimization,"
Optics and Lasers in Engineering, vol.48(12), pp.1213−1223 (maximizes a Tsallis entropybased divergence using modified SPSA; experimental results demonstrate accuracy of proposed approach in comparison to existing entropic image alignment techniques).
Top 
Mostaghimi,
M. (1997), 

"Modeling
Monetary Policy Using SPSABased Neural Networks,"
Proceedings of the IEEE Conference on Decision
and Control, 1012
December 1997, San Diego, CA, pp. 492497
(application in determining macroeconomic policy).
Top

Nandi,
S., Ghosh, S., Tambe, S.S., and Kulkarni, B.D. (2001), 

"Artificial
NeuralNetworkAssisted Stochastic Process Optimization Strategies,"
AIChE Journal, vol. 47, pp. 126141
(process control application; comparisons with genetic algorithms).
Top

Nechyba,
M.C. and Xu, Y. (1997), 

"HumanControl
Strategy: Abstraction, Verification, and Replication,"
IEEE Control Systems Magazine,
vol. 17(5), pp. 4861
(controllers involving humanmachine interaction).
Top

Ni, J. and Song, Q. (2006), 

"Dynamic Pruning Algorithm for Multilayer PerceptronBased Neural Control Systems,"
Neurocomputing, vol. 69, pp. 2097–2111 (use of adaptive SPSA in neural network training).
Top 
Nicolai, R.P. and Koning, A.J. (2006), 

"A General Framework for Statistical Inference on Discrete Event Systems,"
Technical Report EI 200645, Econometric Institute, Erasmus University Rotterdam, The Netherlands (common random numbers for parameter estimation in discrete event systems).
Top 
Ninan, B.M. (2004), 

"Resource Pricing for ConnectionOriented Networks,"
Ph.D. dissertation, North Carolina State University, Operations Research Program, Raleigh, NC (revenue maximization for network pricing).
Top 
Ning, Y., Tang, W., and Wang, H. (2005), 

"Hybrid GeneticSPSA Algorithm Based on Random Fuzzy Simulation for ChanceConstrained Programming,"
in Fuzzy Systems and Knowledge Discovery (L. Wang and Y. Jin, eds.), pp. 332–335, Springer, Berlin (genetic algorithm [GA] is employed to search for the optimal solution in the entire space and SPSA is used to improve the new chromosomes obtained by crossover and mutation at each generation in GA).
Top 
Ning, Y., Tang, W., and Guo, C. (2008), 

"Simultaneous Perturbation Stochastic Approximation Algorithm Combined with Neural Network and Fuzzy Simulation,"
Transactions of Tianjin University, vol. 14(1), pp. 43–49 (SPSA for solving three kinds of fuzzy programming models: fuzzy expected value model, fuzzy chanceconstrained programming model, and fuzzy dependentchance programming model).
Top 
Nusawardhana, N. and Zak, S.H. (2004), 

"Simultaneous
Perturbation Extremum Seeking Method for Dynamic Optimization
Problem,"
Proceedings of the American Control Conference, 29 June–2 July 2004,
Boston, MA, pp. 2805–2810
(application to control problems; includes convergence theory).
Top

Ozguven, E.E. and Ozbay, K (2008), 

"Simultaneous Perturbation Stochastic Approximation Algorithm for Solving Stochastic Problems of Transportation Network Analysis: Performance Evaluation,"
Transportation Research Record: Journal of the Transportation Research Board, no. 2085, pp. 12–20 (comparison with method of successive averages [MSA] in solving traffic assignment problems with varying levels of stochastic effects).
Top 
Palumbo, N.F., Reardon, B.E., and Blauwkamp, R.A.
(2004), 

"Integrated
Guidance and Control for Homing Missiles,"
Johns Hopkins APL Technical Digest, vol. 25, pp. 121–139
(estimation of parameters in a guidance and control model).
Top

Patan,
K. and Parisini, T. (2002), 

"Stochastic
Learning Methods for Dynamic Neural Networks,"
Proceedings of the American Control Conference, 810
May 2002, Anchorage, AK, pp. 25772582
(comparisons of methods based on simulated and real data).
Top

Popovic, D., Jankovic, M., Magner, S., and Teel A.R. (2006), 

"Extremum Seeking Methods for Optimization of Variable Cam Timing Engine Operation,"
IEEE Transactions on Control Systems Technology, vol. 14(3), pp. 398407 (automotive application where common Bernoulli perturbation distribution is modified to satisfy persistent excitation condition in control).
Top 
Poyiadjis, G., Singh, S.S., and Doucet, A. (2006), 

"Gradientfree Maximum Likelihood Parameter Estimation with Particle Filters,"
Proceedings of the American Control Conference, 1416 June 2006, Minneapolis, MN, pp. 3052–3067 (paper ThB08.2) (online estimation of parameters in nonlinear/nonGaussian statespace models with particle filters).
Top 
Primavera, A., Palestini, L., Cecchi, S., Piazza, F., and Moschetti, M. (2010), 

"A Hybrid Approach for RealTime Room Acoustic Response Simulation,"
Audio Engineering Society Convention Paper, presented at the 128th Convention, 22−25 May 2010, London, UK (reverberation algorithm for listening to recorded and live music).
Top 
Rădac, M.B., Precup, R.E., Petriu, E.M., and Preitl, S. (2011), 

"Application of IFT and SPSA to Servo System Control,"
IEEE Transactions on Neural Networks, vol. 22(12), pp. 2363−2375 (considers SPSA combined with iterative feedback tuning for estimating parameters of state feedback controllers in linearquadraticGaussian [LQG] problem formulation; implementation case study concerns LQGbased design of angular position controller for direct current servo system laboratory equipment).
Top 
Ramanathan,
S.P., Mukherjee, S., Dahule, R.K., Ghosh, S., Rahman, I., Tambe,
S.S., Ravetkar, D.D., and Kulkarni, B.D. (2001), 

"Optimization
of Continuous Distillation Columns Using Stochastic Optimization
Approaches,"
Transactions of the Institution of Chemical Engineers,
vol. 79, pp. 310322
(evaluation of SPSA and genetic algorithms in a process control
problem).
Top

Reardon, B.E., Lloyd, J.M., and Perel, R.Y. (2010), 

"Tuning Missile Guidance and Control Algorithms Using Simultaneous Perturbation Stochastic Approximation,"
Johns Hopkins APL Technical Digest, vol. 29(1), pp. 85–100 (automated tuning process for adjustable parameters in guidance and control algorithms for missiles).
Top 
Reardon, B.E., Palumbo, N.F., and Casper, S.G. (2002), 

"SimulationBased
Performance Optimization of Missile Guidance and Control Algorithms,"
11th Annual AIAA/MDA Technology Conference and Exhibit, 29 July2
August 2002, Williamsburg, VA (design of algorithms under constraints;
distribution restricted to U.S. government agencies).
Top

Renjifo, C., Barsic, D., Carmen, C., Norman, K., and Peacock, G.S. (2008), 

"Improving Radial Basis Function Kernel Classification Through Incremental Learning and Automatic Parameter Selection,"
Neurocomputing, vol. 72, pp. 3−14 (support vector machine that employs a greedy search across the training data to select the basis vectors of classifier and tunes parameters using SPSA).
Top 
Renotte,
C., Vande Wouwer, A., and Remy, M. (2000), 

"Neural
Modeling and Control of a Heat Exchanger Based on SPSA Techniques,"
Proceedings of the American Control Conference,
2830
June 2000, Chicago, IL, pp. 32993303
(control application).
Top 
Rezayat,
F. (1995), 

"On
the Use of an SPSAbased ModelFree Controller in Quality Improvement,"
Automatica, vol. 31,
pp. 913915
(operations design and process quality control).
Top

Rezayat,
F. (1999), 

"Constrained
SPSA Controller for Operations Processes,"
IEEE Transactions on Systems, Man, and Cybernetics
— A, vol. 29, pp. 645649
(applies penalty functions to implement constrained SPSA controller
in business application of quality improvement). Top

Sadegh,
P. (1997), 

"Constrained
Optimization via Stochastic Approximation with a Simultaneous Perturbation
Gradient Approximation,"
Automatica, vol. 33,
pp. 889892
(constrained optimization via KuhnTucker considerations).
Top 
Sadegh,
P. and Spall, J.C. (1997), 

"Optimal
Random Perturbations for Stochastic Approximation Using a Simultaneous
Perturbation Gradient Approximation,"
Proceedings of the American Control Conference,
46
June 1997, Albuquerque, NM, pp. 35823586
(guidelines for optimally choosing the distribution of the simultaneous
perturbation vector).
Top

Sadegh,
P. and Spall, J.C. (1998), 

"Optimal
Sensor Configuration for Complex Systems,"
Proceedings of the American Control Conference,
2426
June 1998, Philadelphia, PA, pp. 35753579
(locating and adjusting sensors for maximizing useful information
about an object or process).
Top

Schwartz, J.D. and Rivera, D.E. (2006), 

"SimulationBased Optimal Tuning of Model Predictive Control Policies for Supply Chain Management using Simultaneous Perturbation Stochastic Approximation,"
Proceedings of the American Control Conference, 1416 June 2006, Minneapolis, MN, pp. 556561 (paper WeA16.4) (modelpredictive control as the basis for inventory management policy for supply chains).
Top 
Schwartz, J.D., Rivera, D.E., and Kempf, K.G. (2005),


“Towards
ControlRelevant Forecasting in Supply Chain Management,”
Proceedings of the American Control Conference,
8–10
June 2005, Portland, OR, pp. 202–207
(application to building controller to compensate for demand forecast
error in a manufacturing supply chain).
Top

Schwartz, J.D., Wang, W., and Rivera, D.E. (2006), 

"SimulationBased Optimization of Process Control Policies for Inventory Management in Supply Chains,"
Automatica, vol. 42(8), pp. 13111320 (optimal control applications to management science).
Top 
Sethares, W.A. (2002), 

"RealTime
Adaptive Tunings Using MAX,"
Journal of New Music Research, vol. 31, pp. 347–355
(adaptive tuning algorithm to change the pitch of musical notes
in real time).
Top

Seyedpoora, S.M., Salajeghehb, J., Salajeghehb, E., and Gholizadehc, S. (2011), 

"Optimal Design of Arch Dams Subjected to Earthquake Loading by a Combination of Simultaneous Perturbation Stochastic Approximation and Particle Swarm Algorithms,"
Applied Soft Computing, vol. 11(1), pp, 39−48 (combination of SPSA and particle swarm optimization [PSO] algorithms for finding optimal shapes of arch dams considering fluid–structure interaction subject to earthquake loading).
Top 
Shara, N.M. and Flournoy, N. (2006), 

"Multivariate Optimizing UpandDown Designs,"
Paper presented at Georgetown University, Lombardi Comprehensive Cancer Center, Washington, DC, 15 September 2006 (determining optimal doses for multiple drugs).
Top 
Shekar, S., Smith, A.J., Menz, W.J., Sander, M., and Kraft, M. (2012), 

"A Multidimensional Population Balance Model to Describe the Aerosol Synthesis of Silica Nanoparticles,"
Journal of Aerosol Science, vol. 44, pp. 83–98 (presents population balance model to describe the aerosol synthesis of silica nanoparticles from tetraethoxysilane; free parameters estimated by fitting model response to experimental values of collision and primary particle diameters using low discrepancy Sobol sequences followed by SPSA).
Top 
Sidorov, K., Richmond, S., and Marshall, D. (2009), 

"An Efficient Stochastic Approach to Groupwise Nonrigid Image Registration,"
Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR), Miami, FL, USA, June 2009, pp. 2208−2213 (search for optimal groupwise dense correspondence in large sets of unmarked images).
Top 
Song,
J., Xu, Y., Yam, Y., and Nechyba, M.C. (1998), 

"Optimization
of Human Control Strategy with Simultaneously Perturbed Stochastic
Approximation,"
Proceedings of the IEEE Conference on Intelligent
Robots and Systems,
Part 2, pp. 983988
(controllers involving humanmachine interaction).
Top

Song, Q., Spall, J.C., and Soh, Y.C. (2003), 

"Robust
Neural Network Tracking Controller Using Simultaneous Perturbation
Stochastic Approximation,"
Proceedings of the IEEE Conference on Decision and Control,
912 December 2003, Maui,
Hawaii, pp. 61946199 (modelfree
controller with guaranteed stability in closed loop).
Top

Song, Q., Spall, J.C., and Soh, Y.C. (2008), 

"Robust Neural Network Tracking Controller Using Simultaneous Perturbation Stochastic Approximation,"
IEEE Transactions on Neural Networks, vol. 19(5), pp. 817835 (conic sector theory and SPSA to establish robust neural control system for nonlinear systems).
Top 
Spall,
J.C. (1987), 

"A
Stochastic Approximation Technique for Generating Maximum Likelihood
Parameter Estimates,"
Proceedings of the American Control Conference,
1012
June 1987, Minneapolis, MN, pp. 11611167
(early paper on SPSA).
Top

Spall,
J.C. (1992), 

"Multivariate
Stochastic Approximation Using a Simultaneous Perturbation Gradient
Approximation,"
IEEE Transactions on Automatic Control,
vol. 37, pp. 332341
(core paper on theoretical and numerical properties).
Top 
Spall,
J.C. (1994), 

"Developments
in Stochastic Optimization Algorithms with Gradient Approximations
Based on Function Measurements,"
Proceedings of the Winter Simulation Conference
(J.D. Tew, M.S. Manivannan, D.A. Sadowski, and A.F. Seila, eds.) pp.
207214
(review of several approaches in gradientfree setting).
Top 
Spall,
J.C. (1997), 

"A
OneMeasurement Form of Simultaneous Perturbation Stochastic Approximation,"
Automatica, vol. 33, pp. 109112
(uses gradient estimate based on only one function measurement with
potential applications with timevarying loss functions).
Top

Spall,
J.C. (1998), 

"Implementation
of the Simultaneous Perturbation Algorithm for Stochastic Optimization,"
IEEE Transactions on Aerospace and Electronic Systems,
vol. 34, pp. 817823
(guidelines for practical implementation and choice of gain coefficients).
Top

Spall,
J.C. (1998), 

"An
Overview of the Simultaneous Perturbation Method for Efficient Optimization,"
Johns Hopkins APL Technical Digest,
vol. 19, pp. 482492
(survey paper on SPSA).
Top 
Spall,
J.C. (2000), 

"Adaptive
Stochastic Approximation by the Simultaneous Perturbation Method,"
IEEE Transactions on Automatic Control,
vol. 45, pp. 18391853
(gradientfree and gradientbased methods for obtaining nearoptimal
or optimal convergence rates via stochastic analogues to deterministic
NewtonRaphson algorithm; Hessian matrix estimation).
Top

Spall, J.C. (2005), 

"Monte
Carlo Computation of the Fisher Information Matrix in Nonstandard
Settings,"
Journal of Computational and Graphical Statistics (American
Statistical Assoc.),
vol. 14(4), pp. 889909
(use
of simultaneous perturbationbased Hessian estimation for easy calculation of the Fisher
information matrix [as appears, e.g., in CramérRao bound] in general
nonlinear problems, including analysis of antithetic random
numbers).
Top

Spall, J.C. (2009), 

"Feedback and Weighting Mechanisms for Improving Jacobian Estimates in the Adaptive Simultaneous Perturbation Algorithm,"
IEEE Transactions on Automatic Control,
vol. 54(6), pp. 12161229
(method for improving the Jacobian [or Hessian] estimate in the adaptive SPSA method).
Top 
Spall,
J.C and Chin, D.C. (1997), 

"TrafficResponsive
Signal Timing for SystemWide Traffic Control,"
Transportation Research—Part C,
vol. 5, pp. 153163
(use in building signaltiming control algorithm for traffic network).
Top

Spall,
J.C. and Cristion, J.A. (1994), 

"Nonlinear
Adaptive Control Using Neural Networks: Estimation With a Smoothed
Form of Simultaneous Perturbation Gradient Approximation,"
Statistica Sinica, vol.
4, pp. 1 27
(adaptive control and "smoothed" gradient approximation).
Top 
Spall,
J.C. and Cristion, J.A. (1997), 

"A
Neural Network Controller for Systems with Unmodeled Dynamics with
Applications to Wastewater Treatment,"
IEEE Transactions on Systems, Man, and Cybernetics—B, vol. 27, pp. 369 375
(control application and neural network training).
Top

Spall,
J.C. and Cristion, J.A. (1998), 

"ModelFree
Control of Nonlinear Stochastic Systems with DiscreteTime Measurements,"
IEEE Transactions on Automatic Control,
vol. 43, pp. 11981210
(establishes formal convergence of SPSAbased controller; also illustrates
numerical properties).
Top 
Spall, J.C., Hill, S.D., and Stark, D.R. (2006),


"Theoretical
Framework for Comparing Several Stochastic Optimization Approaches,"
in Probabilistic and Randomized Methods for Design under Uncertainty
(G. Calafiore and F. Dabbene, eds.), Springer, Berlin,
Chapter 3 (some comparative theoretical insight into random search,
SPSA, simulated annealing, and evolution strategies).
Top

Srinivasan, D., Choy, M.C., and Cheu, R.L. (2006), 

"Neural Networks for RealTime Traffic Signal Control,"
IEEE Transactions on Intelligent Transportation Systems, vol. 7(3), pp. 261272 (distributed multiagent control for urban traffic management and signal timing).
Top 
Steenis, R. and Rivera, D.E. (2011), 

“PlantFriendly Signal Generation for System Identification Using a Modified Simultaneous Perturbation Stochastic Approximation (SPSA) Methodology,”
IEEE Transactions on Control Systems Technology, vol. 19(6), pp.1604−1612 (considers modified SPSA version [MSPSAK] that perturbs signal phase parameters in K subsets rather than simultaneously; method can be applied to signals with arbitrarily defined spectrum in both amplitude and frequency).
Top 
Sultan, I. and Puthiyaveettil, P. (2012), 

“Calibration of an Articulated CMM Using Stochastic Approximations,”
The International Journal of Advanced Manufacturing Technology, published online 17 January 2012 (coordinate measuring machine: identify the parameters of the kinematic model in order for the accurate performance to be achieved; demonstration on fiveaxis revolutejoint serial manipulator robot with high degree of dexterity).
Top 
Sultan, I.A. and Schaller C.G. (2011), 

"Optimum Positioning of Ports in the Limaçon Gas Expanders,"
Journal of Engineering for Gas Turbines and Power—Transactions of the ASME, vol. 133(10), pp. 1030021 − 10300211 (positive displacement expanders are used in the fields of micropower generation and refrigeration engineering; SPSA is used to find the locations for the expander ports that produce the best expander performance).
Top 
Sun, C., Hirata, A., Ohira, T., Karmakar, N.C. (2004), 

"Fast
Beamforming of Electronically Steerable Parasitic Array Radiator
Antennas: Theory and Experiment,"
IEEE Transactions on Antennas and Propagation, vol. 52(7),
pp. 1819–1832
(optimal beamforming in antenna design).
Top

Taflanidis, A. A. and Beck, J. L. (2008), 

"An Efficient Framework for Optimal Robust Stochastic System Design Using Stochastic Simulation,"
Computer Methods in Applied Mechanics and Engineering, vol. 198, pp. 88–101 (provides details on how stochastic subset optimization can be efficiently combined with SPSA for controller design; example in optimization of baseisolation system for threestory structure in face of earthquake excitations).
Top 
Tayong,
H., Beasley, A., ColeRhodes, A., and Cooper, A.B. (2002), 

"Adaptive
Optimization of a Parametric Receiver for Fast FrequencyHopping,"
36th Annual Conference on Information Sciences
and Systems, 2022
March 2002, Princeton, NJ, paper no. 180 (CDROM Proceedings) (signal
processing application).
Top

Thangavel, P. and Kathirvalavakumar, T. (2003), 

"Simultaneous
Perturbation for Single Hidden Layer Networks—Cascade Learning,"
Neurocomputing, vol. 50, pp. 193–209
(training in single layer neural networks).
Top 
Ting,
C.J. and Schonfeld, P. (1998),


"Optimization
through Simulation of Waterway Transportation Investments,"
Transportation Research Record,
no. 1620, pp. 11 16
(example of simulationbased optimization for longterm planning
of waterway network capacity).
Top 
Tsakalaki, E.P. Alrabadi, O.N. Papadias, C.B. Prasad, R. (2011), 

"Adaptive ReactanceControlled Antenna Systems for MultiInput MultiOutput Applications,"
IET Microwaves, Antennas and Propagation, vol. 5(8), pp. 975−984 (considers multiinput multioutput systems under reallife effects of spatial correlation and antenna mutual coupling; aim to maximize the communication rate).
Top 
Vakhitov, A.T., Granichin, O.N., and Sysoev, S.S. (2006), 

"A Randomized Stochastic Optimization Algorithm: Its Estimation Accuracy,"
Automation and Remote Control, vol. 67(4), pp. 589597 (possible SPSA implementation in quantum computing).
Top 
Vande Wouwer, A. and Renotte, C. (2003), 

"Stochastic
Approximation Techniques Applied to Parameter Estimation in a
Biological Model,"
Proceedings of the IEEE Conference on Intelligent Data Acquisition
and Advanced Computing Systems: Technology and Applications,
Lviv, Ukraine, 911 September
2003 (nonlinear system identification for biological models).
Top 
Vande
Wouwer, A., Renotte, C., and Remy, M. (1999), 

"On
the Use of Simultaneous Perturbation Stochastic Approximation for
Neural Network Training,"
Proceedings of the American Control Conference, 24
June 1999, San Diego, CA, pp. 388392
(experiments with first and secondorder SPSA).
Top 
Vande Wouwer, A., Renotte, C., and Remy, M. (2003),


"Application
of Stochastic Approximation Techniques in Neural Modelling and
Control,"
International Journal of Systems Science, vol. 34, pp. 851–863
(modifications of basic algorithm for use in neural network training).
Top

Vande
Wouwer, A., Renotte, C., Bogaerts, Ph., and Remy, M. (2001), 

"Application
of SPSA Techniques in Nonlinear System Identification,"
European Control Conference, 47
September 2001, Porto, Portugal (SPSA for control of bioprocesses).
Top 
Vande Wouwer, A., Renotte, C., and Bogaerts, P.H. (2006), 

"A Short Note on SPSA Techniques and Their use in Nonlinear Bioprocess Identification,"
Mathematical and Computer Modelling of Dynamical Systems, vol.12(5), pp. 415–422 (considers use of adaptive gain sequences, illustrating approach in context of a bioprocess model describing the evolution of batch animal cell cultures).
Top 
Vaze, V., Antoniou, C., Wen, Y., and BenAkiva, M. (2009), 

"Calibration of Dynamic Traffic Assignment Models with PointtoPoint Traffic Surveillance,"
Transportation Research Record: Journal of the Transportation Research Board, No. 2090, pp. 1–9 (comparison of SPSA and GA in calibration of demand and supply simulators for dynamic traffic assignment for use in providing consistent travel information and in efficient traffic management).
Top 
Velusamy, S., Bhatnagar, S., Basavaraja, S.V., and Sridhar, V. (2008), 

"SPSA Based Feature Relevance Estimation for Video Retrieval,"
Proceedings of the IEEE 10th Workshop on Multimedia Signal Processing (MMSP), 8−10 October 2008, Cairns, Qld, Australia, pp. 598−603 (interactive video retrieval with efficient indexing from features such as color, texture, face, and audio information; optimizes feature weights in contentbased video retrieval).
Top 
Venkatesh, Y.V., Kassim, A.A., and Zonoobi, D. (2010), 

"Medical Image Reconstruction from Sparse Samples using Simultaneous Perturbation Stochastic Optimization,"
17th IEEE International Conference on Image Processing (ICIP), 26−29 Sept. 2010, Hong Kong, pp. 3369−3372 (approach for Lpnorm [p < 1] reconstruction of medical images from compressive samples in either the spatial or transformed domain; demonstration on real and simulated images).
Top 
Vitsentiy,
V. (2002), 

"Improvement
of HumanMachine Interaction with Applications to Information Retrieval
System,"
Proceedings of the First International IEEE Symposium
on Intelligent Systems, 1012 September 2002, Varna, Bulgaria
(adaptive control involving humanmachine interaction).
Top 
Vorontsov,
M.A., Carhart, G.W., Cohen, M., and Cauwenberghs, G. (2000), 

"Adaptive
Optics Based on Analog Parallel Stochastic Optimization: Analysis
and Experimental Demonstration,"
Journal of the Optical Society of America A,
vol. 17, pp. 14401453
(application in adaptive opticalbased control system).
Top

Vorontsov, M.A. and Carhart, G.W. (2006), 

"Adaptive Wavefront Control with Asynchronous Stochastic Parallel Gradient Descent Clusters,"
Journal of the Optical Society of America A, vol. 23(10), pp. 2613–2622 (shows that division of controls into asynchronous clusters improves the system performance in an adaptive optics system).
Top 
Wang,
I.J. and Chong, E.K.P. (1996), 

"A
Deterministic Analysis of Simultaneous Perturbation Stochastic Approximation,"
Proceedings of the 30th Conference on Information
Sciences and Systems, pp. 918922
(convergence analysis via deterministic methods).
Top

Wang,
I.J. and Chong, E.K.P. (1998), 

"A
Deterministic Analysis of Stochastic Approximation with Randomized
Directions,"
IEEE Transactions on Automatic Control,
vol. 43, pp. 17451749
(convergence analysis of SPSA and random directions SA via deterministic
methods).
Top 
Wang, I.J. and Spall, J.C. (2003), 

"Stochastic
Optimization with Inequality Constraints Using Simultaneous Perturbations
and Penalty Functions,"
Proceedings of the IEEE Conference on Decision
and Control, 912
December 2003, Maui, Hawaii, pp. 38083813
(method for handling general constraints; includes convergence and
asymptotic distribution theory).
Top 
Wang, I.J. and Spall, J.C. (2008), 

"Stochastic Optimization with Inequality Constraints Using Simultaneous Perturbations and Penalty Functions,"
International Journal of Control,
vol. 81(8), pp. 12321238 (updated version of above 2003 CDC paper; method for handling general constraints; includes convergence analysis, asymptotic distribution theory, and numerical example).
Top 
Wang, L. and Prabhu, V. (2009), 

"A Stochastic Perturbation Algorithm for Inventory Optimization in Supply Chains,"
International Journal of Information Systems and Supply Chain Management, vol. 2(3), pp. 118 (considers an augmented SPSA to include ordinal optimization, nonuniform gain, and line search; comparison with genetic algorithm).
Top 
Wang, Q. and Spall, J.C. (2011), 

“Discrete Simultaneous Perturbation Stochastic Approximation on Loss Functions with Noisy Measurements,”
Proceedings of the American Control Conference, 29 June1 July 2011, San Francisco, CA, pp. 4520−4525 (paper FrB10.3) (method for optimization of discrete functions in the presence of noisy function measurements).
Top 
Webster,
T.M. (1988), 

"Some
Experience with Stochastic Approximation Algorithms in LargeScale
Systems,"
Proceedings of the American Statistical Association,
Statistical Computing Section, August
1988, New Orleans, LA, pp. 181186
(some early numerical experiments).
Top 
Weyrauch,
T. and Vorontsov, M.A. (2002), 

"Dynamic
WaveFront Distortion Compensation with a 134ControlChannel Submillisecond
Adaptive System,"
Optics Letters, vol. 27, pp. 751753
(application in adaptive optics system). Top 
Whitney,
J.E. and Hill, S.D. (2001), 

"Constrained
Optimization Over Discrete Sets via SPSA with Application to NonSeparable
Resource Allocation,"
Proceedings of the Winter Simulation Conference,
912
December 2001, Arlington, VA, pp. 313317
(application of SPSA in discrete optimization).
Top

Whitney,
J.E., Duncan, K., Richardson, M., and Bankman, I. (2000), 

"Parameter
Estimation in a Highly Nonlinear Model Using Simultaneous Perturbation
Stochastic Approximation,"
Communications in Statistics—Theory and Methods,
vol. 29, pp. 12471256
(use of first and secondorder SPSA in a physical model).
Top

Xing,
X.Q. and Damodaran, M. (2002), 

"Assessment
of Simultaneous Perturbation Stochastic Approximation Method for
Wing Design Optimization,"
Journal of Aircraft (AIAA),
vol. 39, pp. 379381
(comparison with simulated annealing and genetic algorithms
on an aircraft design problem).
Top 
Xing, X.Q. and Damodaran, M. (2005), 

"Application
of Simultaneous Perturbation Stochastic Approximation Method for
Aerodynamic Shape Design Optimization,"
AIAA Journal, vol. 43, pp. 284–294
(SPSA is compared with simulated annealing for a class of aerodynamic
design optimization problems).
Top

Xing, X.Q. and Damodaran, M. (2005), 

"Inverse
Design of Transonic Airfoils Using Parallel Simultaneous Perturbation
Stochastic Approximation,"
Journal of Aircraft (AIAA), vol. 42(2), pp. 568–570
(a parallel version of SPSA to deal with inverse airfoil design
problem).
Top

Xiong, X., Wang, I.J. and Fu, M.C. (2002), 

"An Asymptotic
Analysis of Stochastic Approximation with Deterministic Perturbation
Sequences,"
Proceedings of the Winter Simulation Conference, 811
December 2002, San Diego, CA, pp. 285291
(use of deterministic—vs. random—perturbation vectors).
Top

Xu, P., Li, G., and Wang, K. (2012), 

"Self Tuning of PID Controller Based on Simultaneous Perturbation Stochastic Approximation," in Advances in Electronic Engineering, Communication and Management Vol.1 (D. Jin and S. Lin, eds.), Lecture Notes in Electrical Engineering 139, pp. 647–652 (online tuning of parameters of a PID controller without assuming model).
Top 
Xu,
Y., Song, J., Nechyba, M.C., Yam, Y. (2002), 

"Performance
Evaluation and Optimization of Human Control Strategy,"
Robotics and Autonomous Systems, vol. 39(1), pp. 1936
(controllers involving humanmachine interaction).
Top 
Yakovlev, V. and Tempea, G. (2002), 

"Optimization
of Chirped Mirrors,"
Applied Optics—LP, vol. 41, pp. 65146520
(optimization for the design of dielectric multilayer mirrors).
Top

Yang, J.S. (2004), 

"Traffic Signal Timing Control for a SmallScale Road Network,"
Proceedings of the 6th IASTED International Conference on Control and Applications, 13 March 2004, Marina Del Rey (Los Angeles), California, USA, pp. 117122 (paper 441048) (pilot study of the development and evaluation of a traffic signal timing control for a small scale road network in downtown Duluth, Minnesota).
Top 
Yang, J.S. (2008), 

"An OptimizationBased Approach to SpecialEvents Traffic Signal Timing Control,"
Control and Intelligent Systems, vol. 36(2), paper no. 2011690 (SPSA and neural nets for signal control in the face of a sudden traffic surge immediately after special events such as conventions, sporting events, or concerts).
Top 
Yin,
G., Zhang, Q., Yan, H.M., and Boukas, E.K. (2001), 

"Random
Direction Optimization Algorithms with Applications to Threshold
Controls,"
Journal of Optimization Theory and Applications,
vol. 110, pp. 211233
(application in a constrained optimal control problem).
Top

Yuan. Q.H. (2008), 

"A Model Free Automatic Tuning Method for a Restricted Structured Controller by Using Simultaneous Perturbation Stochastic Approximation (SPSA),"
Proceedings of the American Control Conference, 1113 June 2008, Seattle, Washington, USA, pp. 15391545 (paper WeC09.5) (automatic tuning of PID controllers, with example in electrohydraulic valve).
Top 
Yue, X. (2008), 

"Improved Simultaneous Perturbation Stochastic Approximation and its Application in Reinforcement Learning,"
Proceedings of the 2008 International Conference on Computer Science and Software Engineering, vol. 1, pp. 329−332, 12−14 December 2008 (uses nonlinear conjugate gradient and reinforcement learning method to improve SPSA convergence).
Top 
Yue, Y. and Burges, C. J. C. (2007), 

"On Using Simultaneous Perturbation Stochastic Approximation for IR Measures, and the Empirical Optimality of LambdaRank,"
NIPS Machine Learning for Web Search Workshop, 7 December 2007, Whistler, Canada (investigation of whether gradient of information retrieval performance measures, such as normalized discounted cumulative gain, might be numerically approximated given discrete nature of objective function).
Top 
Zein, S., Canot, E., Erhel, J., and Nassif, N. (2008), 

"Determination of the Mechanical Properties of a Solid Elastic Medium from a Seismic Wave Propagation Using Two Statistical Estimators,"
Mathematics and Mechanics of Solids, vol. 13(5), pp. 388407 (estimation of mechanical parameters for inverse problem consisting in the determination of the mechanical properties of a layered solid elastic medium in contact with a fluid medium; comparison with MCMC).
Top 
Zhang, J., Zhao, R., and Tang, W. (2008), 

"Fuzzy AgeDependent Replacement Policy and SPSA Algorithm Based on Fuzzy Simulation,"
Information Sciences: An International Journal, vol. 178(2), pp. 573583 (estimation for problem of agedependent replacement policy in maintenance using a fuzzy simulation technique to estimate the expected value of the objective function).
Top 
Zhao, H., Li, Y., Yao, J., and Zhang, K. (2011), 

“Theoretical Research on Reservoir ClosedLoop Production Management,”
Science in China Series E: Technological Sciences, vol. 54(10), pp. 2815−2824 (reservoir closedloop production management; demonstrated reduced geological uncertainty and provided reasonable estimate of reservoir model without calculation of adjointgradient).
Top 
Zhou, Y.L., Zhang, Q.Z., Li, X.D., Gan, W.S. (2008), 

"On the use of an SPSAbased modelfree feedback controller in active noise control for periodic disturbances in a duct,"
Journal of Sound and Vibration, vol. 317, pp. 456472
(feedback active noise control system using a modelfree controller). 
Zhu,
X. (2001), 

"Matrix Conditioning and Adaptive Simultaneous Perturbation Stochastic Approximation Method,"
Proceedings of the American Control Conference,
2527
June 2001, Arlington, VA, pp. 13891395
(modified form of adaptive ["secondorder"] SPSA).
Top

Zhu, X. and Spall, J.C. (2002), 

"A
Modified SecondOrder SPSA Optimization Algorithm for Finite Samples,"
International Journal of Adaptive Control and
Signal Processing, vol. 16, pp. 397409
(modified form of adaptive [“secondorder”] SPSA).
Top 
Zonoobi, D., Kassim, A.A., Venkatesh, Y.V. (2011), 

"Gini Index as Sparsity Measure for Signal Reconstruction from Compressive Samples,"
IEEE Journal of Selected Topics in Signal Processing, vol. 5(5), pp. 927−932 (compressive sensing; reconstruction of a discrete signal from a set of incomplete observations using Gini index as measure of sparsity).
Top 



