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A Stochastic Approximation Method
IEEE Transactions on Systems, Man, and Cybernetics, 1971A new algorithm for stochastic approximation has been proposed, along with the assumptions and conditions necessary for convergence. It has been proved by two different methods that the algorithm converges to the sought value in the mean-square sense and with probability one.
Sinha, Naresh K., Griscik, Michael P.
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On approximate stochastic realization
Mathematics of Control, Signals, and Systems, 1991zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1996
This chapter deals with algorithms for the optimization of simulated systems.In particular we study stochastic variants of the gradient algorithm xn+1=xn−an∇F(xn)] which was introduced in (1.27) to solve the optimization problem [F(x)=∥∥∥MinimizeF(x)x∈Rd] where F is bounded from below.
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This chapter deals with algorithms for the optimization of simulated systems.In particular we study stochastic variants of the gradient algorithm xn+1=xn−an∇F(xn)] which was introduced in (1.27) to solve the optimization problem [F(x)=∥∥∥MinimizeF(x)x∈Rd] where F is bounded from below.
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Randomized Stochastic Approximation
2015Multidimensional stochastic optimization plays an important role in the analysis and control of many technical systems. Randomized algorithms of stochastic approximation with perturbed input have been suggested for solving the challenging multidimensional problems of optimization.
Oleg Granichin +2 more
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Stochastic Approximation Algorithms
2013Stochastic approximation algorithms have been one of the main focus areas of research on solution methods for stochastic optimization problems. The Robbins-Monro algorithm [17] is a basic stochastic approximation scheme that has been found to be applicable in a variety of settings that involve finding the roots of a function under noisy observations ...
S. Bhatnagar, H. Prasad, L. Prashanth
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Stochastic Approximation, with Applications
2003Optimization is ubiquitous in various research and application fields. Many theoretical and practical problems are often reduced to optimizing some function L(·), i.e., finding its minimum (or maximum).
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1984
Publisher Summary This chapter provides information on the stochastic approximation method. The chapter reveals the procedure that was proposed and investigated first by Robbins and Monro and called a stochastic approximation method. Practically all the asymptotic properties of the Robbins–Monro procedure (including the asymptotic normality) can be ...
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Publisher Summary This chapter provides information on the stochastic approximation method. The chapter reveals the procedure that was proposed and investigated first by Robbins and Monro and called a stochastic approximation method. Practically all the asymptotic properties of the Robbins–Monro procedure (including the asymptotic normality) can be ...
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