Extensions of Stochastic Optimization Results to Problems with System Failure Probability Functions

We derive an implementable algorithm for solving nonlinear stochastic optimization problems with failure probability constraints using sample average approximations. The paper extends prior results dealing with a failure probability expressed by a single measure to the case of failure probability expressed in terms of multiple performance measures. We also present a new formula for the failure probability gradient. A numerical example addressing the optimal design of a reinforced concrete highway bridge illustrates the algorithm. This work was sponsored by the Research Associateship Program, National Research Council. The authors are grateful for the valuable insight from Professors Alexander Shapiro, Evarist Gine, and Jon A. Wellner. The authors also thank Professor Tito Homem-de-Mello for commenting on an early draft of this paper.