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Stochastic approximation type methods for constrained systems: Algorithms and numerical results

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2 Author(s)
H. Kushner ; Brown University, Providence, RI, USA ; T. Gavin

A stochastic version of the standard nonlinear programming problem is considered. A function f(x) is observed in the presence of noise, and we seek to minimize f(x) for x \in C = {x:q^{i}(x) \leq 0} , where q^{i}(x) are constraints. Numerous practical examples exist. Algorithms are discussed for selecting a sequence Xnwhich converges wp 1 to a point where a necessary condition for optimality holds. The algorithms use, of course, noise-corrupted observations on the f(x) . Numerical results are presented. They indicate that the approach is quite versatile, and can be a useful tool for systematic Monte-Carlo optimization of constrained systems, a much-neglected area. However, many practical problems remain to be resolved, e.g., investigation of efficient one-dimensional search methods and of the tradeoffs between the effort spent per search cycle and the number of search cycles.

Published in:

IEEE Transactions on Automatic Control  (Volume:19 ,  Issue: 4 )