Expected Value and Sample Average Approximation Method for Solving Stochastic Second-Order Cone Complementarity Problems

Abstract

ABSTRACTIn this paper, we consider the stochastic second-order cone complementarity problems (SSOCCP). We first formulate the SSOCCP contained expectation as an optimization problem using the so-called second-order cone complementarity function. We then use sample average approximation method and smoothing technique to obtain the approximation problems for solving this reformulation. In theory, we show that any accumulation point of the global optimal solutions or stationary points of the approximation problems are global optimal solution or stationary point of the original problem under suitable conditions. Finally, some numerical examples are given to explain that the proposed methods are feasible.