CONVERGENCE ANALYSIS OF A REGULARIZED SAMPLE AVERAGE APPROXIMATION METHOD FOR STOCHASTIC MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

摘要

Regularization method proposed by Scholtes (2011) has been a recognized approach for deterministic mathematical programs with complementarity constraints (MPCC). Meng and Xu (2006) applied the approach coupled with Monte Carlo techniques to solve a class of one stage stochastic MPCC and presented some promising numerical results. However, Meng and Xu have not presented any convergence analysis of the regularized sample approximation method. In this paper, we fill out this gap. Specifically, we consider a general class of one stage stochastic mathematical programs with complementarity constraint where the objective and constraint functions are expected values of random functions. We carry out extensive convergence analysis of the regularized sample average approximation problems including the convergence of statistical estimators of optimal solutions, C-stationary points, M-stationary points and B-stationary points as sample size increases and the regularization parameter tends to zero.