Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization

摘要

In this paper, we consider the stochastic mathematical programs with linear complementarity constraints, which include two kinds of models called here-and-now and lower-level wait-and-see problems. We present a combined smoothing implicit programming and penalty method for the problems with a finite sample space. Then, we suggest a quasi-Monte Carlo approximation method for solving a problem with continuous random variables. A comprehensive convergence theory is included as well. We further report numerical results with the so-called picnic vender decision problem. Keywords Stochastic mathematical program with equilibrium constraints - Wait-and-see - Here-and-now - Smoothing implicit programming - Quasi-Monte Carlo method Mathematics Subject Classification (2000) 90C30 - 90C33 - 90C15 This work was supported in part by the Scientific Research Grant-in-Aid from Japan Society for the Promotion of Science.