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

A stochastic version of the standard nonlinear programming problem is considered. A function is observed in the presence of noise, and we seek to minimize for , where 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 . 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.