Stochastic Optimization, Stochastic Approximation and Simulated Annealing

The sections in this article are 1 Robbins–Monro Stochastic Approximation 2 Stochastic Approximation with Gradient Approximations Based on Function Measurements 3 Simultaneous Perturbation Stochastic Approximation 4 Simulated Annealing 5 Concluding Remarks 6 Acknowledgements

[1]  S. Mitter,et al.  Simulated annealing with noisy or imprecise energy measurements , 1989 .

[2]  J. Blum Approximation Methods which Converge with Probability one , 1954 .

[3]  H. White Some Asymptotic Results for Learning in Single Hidden-Layer Feedforward Network Models , 1989 .

[4]  A new normalized stochastic approximation algorithm using a time‐shift parameter , 1995 .

[5]  Fahimeh Rezayat On the use of an SPSA-based model-free controller in quality improvement , 1995, Autom..

[6]  Kurt Hornik,et al.  Convergence of learning algorithms with constant learning rates , 1991, IEEE Trans. Neural Networks.

[7]  James C. Spall,et al.  A one-measurement form of simultaneous perturbation stochastic approximation , 1997, Autom..

[8]  H. Kushner,et al.  Stochastic approximation with averaging of the iterates: Optimal asymptotic rate of convergence for , 1993 .

[9]  M. A. Styblinski,et al.  Experiments in nonconvex optimization: Stochastic approximation with function smoothing and simulated annealing , 1990, Neural Networks.

[10]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Michael L. Lightstone,et al.  A new efficient approach for the removal of impulse noise from highly corrupted images , 1996, IEEE Trans. Image Process..

[12]  George Ch. Pflug,et al.  Optimization of Stochastic Models , 1996 .

[13]  P. Glynn,et al.  Stochastic Optimization by Simulation: Convergence Proofs for the GI/G/1 Queue in Steady-State , 1994 .

[14]  D. C. Chin,et al.  Comparative study of stochastic algorithms for system optimization based on gradient approximations , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[15]  C. Z. Wei Multivariate Adaptive Stochastic Approximation , 1987 .

[16]  S. Evans,et al.  On the almost sure convergence of a general stochastic approximation procedure , 1986, Bulletin of the Australian Mathematical Society.

[17]  G. Pflug Stochastic minimization with constant step-size: asymptotic laws , 1986 .

[18]  Terrence L. Fine,et al.  Online Steepest Descent Yields Weights with Nonnormal Limiting Distribution , 1996, Neural Computation.

[19]  S. Mitter,et al.  Metropolis-type annealing algorithms for global optimization in R d , 1993 .

[20]  Boris Polyak,et al.  Acceleration of stochastic approximation by averaging , 1992 .

[21]  Michael C. Fu,et al.  Conditional Monte Carlo , 1997 .

[22]  H. Kushner,et al.  Stochastic approximation with averaging and feedback: rapidly convergent "on-line" algorithms , 1995, IEEE Trans. Autom. Control..

[23]  Gang George Yin,et al.  Budget-Dependent Convergence Rate of Stochastic Approximation , 1995, SIAM J. Optim..

[24]  R. Suri,et al.  Perturbation analysis: the state of the art and research issues explained via the GI/G/1 queue , 1989, Proc. IEEE.

[25]  V. Fabian Simulated annealing simulated , 1997 .

[26]  J. Sacks Asymptotic Distribution of Stochastic Approximation Procedures , 1958 .

[27]  J. Blum Multidimensional Stochastic Approximation Methods , 1954 .

[28]  Yutaka Maeda,et al.  A learning rule of neural networks via simultaneous perturbation and its hardware implementation , 1995, Neural Networks.

[29]  H. Kushner,et al.  Asymptotic Properties of Stochastic Approximations with Constant Coefficients. , 1981 .

[30]  R. Vidal Applied simulated annealing , 1993 .

[31]  J. H. Venter An extension of the Robbins-Monro procedure , 1967 .

[32]  James C. Spall,et al.  A neural network controller for systems with unmodeled dynamics with applications to wastewater treatment , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[33]  V. Fabian On Asymptotic Normality in Stochastic Approximation , 1968 .

[34]  D. L. Hanson,et al.  Almost Sure Convergence for the Robbins-Monro Process , 1976 .

[35]  S. Brooks,et al.  Optimization Using Simulated Annealing , 1995 .

[36]  Bernard Delyon,et al.  Accelerated Stochastic Approximation , 1993, SIAM J. Optim..

[37]  John N. Tsitsiklis,et al.  Analysis of Temporal-Diffference Learning with Function Approximation , 1996, NIPS.

[38]  G. Yin,et al.  Asymptotic optimal rate of convergence for an adaptive estimation procedure , 1992 .

[39]  Lennart Ljung,et al.  Analysis of recursive stochastic algorithms , 1977 .

[40]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[41]  D. Ruppert A Newton-Raphson Version of the Multivariate Robbins-Monro Procedure , 1985 .

[42]  G. Yin,et al.  Passive stochastic approximation with constant step size and window width , 1996, IEEE Trans. Autom. Control..

[43]  Payman Sadegh,et al.  Constrained optimization via stochastic approximation with a simultaneous perturbation gradient approximation , 1997, Autom..

[44]  H. Kesten Accelerated Stochastic Approximation , 1958 .

[45]  J. Kiefer,et al.  Stochastic Estimation of the Maximum of a Regression Function , 1952 .

[46]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[47]  J. Spall Multivariate stochastic approximation using a simultaneous perturbation gradient approximation , 1992 .