Stochastic Ellipsoid Methods for Robust Feasibility Problems with Multiple Constraints

Abstract

A stochastic ellipsoid method is proposed for a class of robust feasibility problems defined by a set of parameter-dependent convex constraints.In particular, a new update rule is presented for constructing a smaller ellipsoid which contains the intersection of the previous ellipsoid and strips determined by given multiple gradients, which leads to reduction of the total number of random samples necessary for convergence.