Regularization method for stochastic mathematical programs with complementarity constraints

¹ Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China; ghlin@amp.i.kyoto-u.ac.jp
² Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan; fuku@amp.i.kyoto-u.ac.jp

Received: 5 December 2003
Revised: 7 July 2004

Abstract

In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs) that has been discussed by Lin and Fukushima (2003). Based on a reformulation given therein, we propose a regularization method for solving the problems. We show that, under a weak condition, an accumulation point of the generated sequence is a feasible point of the original problem. We also show that such an accumulation point is S-stationary to the problem under additional assumptions.