Sequential Randomized Algorithms for Robust Optimization

Abstract

A probabilistic approach is considered for robust optimization, where a convex objective function is minimized subject to a parameter dependent convex constraint. A randomized algorithm is proposed for solving this optimization employing the stochastic ellipsoid method, where an optimality cut which describes a provisional optimal value is sequentially updated. It is shown that the upper bounds of the numbers of random samples and updates of the algorithm are of polynomial order of the problem size and much less than those of the stochastic bisection method utilizing the stochastic ellipsoid method at each iteration. This feature actually leads to a computational advantage, which is demonstrated through a numerical example.