Solution to Robust Two-Stage Stochastic Convex Programming Using Subgradient Method

Abstract

A robust two-stage stochastic convex programming model is proposed in this paper with the second stage of which is quadratic programming. A formula is obtained to calculate the subdifferential of the recourse function, under the assumption that linear partial information is observed for the probability distribution. A subgradient algorithm based on deflected subgradients and exponential decay step sizes is proposed to solve the robust stochastic convex programming problem. The convergence of the algorithm is proved, and the effectiveness is demonstrated by the numerical examples.