Gaining traction: on the convergence of an inner approximation scheme for probability maximization

Abstract

AbstractWe analyze an inner approximation scheme for probability maximization. The approach was proposed in Fábián et al. (Acta Polytech Hung 15:105–125, 2018), as an analogue of a classic dual approach in the handling of probabilistic constraints. Even a basic implementation of the maximization scheme proved usable and endured noise in gradient computations without any special effort. Moreover, the speed of convergence was not affected by approximate computation of test points. This robustness was then explained in an idealized setting. Here we work out convergence proofs and efficiency arguments for a nondegenerate normal distribution. The main message of the present paper is that the procedure gains traction as an optimal solution is approached.