Implementable Algorithm for Stochastic Optimization Using Sample Average Approximations

Abstract

We develop an implementable algorithm for stochastic optimization problems involving probability functions. Such problems arise in the design of structural and mechanical systems. The algorithm consists of a nonlinear optimization algorithm applied to sample average approximations and a precision-adjustment rule. The sample average approximations are constructed using Monte Carlo simulations or importance sampling techniques. We prove that the algorithm converges to a solution with probability one and illustrate its use by an example involving a reliability-based optimal design.