New Approximation Approach for Stochastic Programming Problems with Probability Function

Abstract

Many practical problems can be formalized as optimization problems with a probability function in its objective or in constraints. But only for linear cases the optimization technique is well developed for solving these problems [2, 3, 6]. Generally, difficulties arise since we can not represent the probability function analytically or in the form of expectation of a smooth function. In [1, 2, 3, 6, 7, 8] numerical methods based on some estimations of the probability function and its gradient are suggested. Most of them have low convergence rate because they need expensive calculations for estimating the probability function and its gradient at every point.