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

• 成果类型: Article; Proceedings Paper
• 署名作者: Lin, Gui-Hua; Chen, Xiaojun; Fukushima, Masao
• 署名单位: Kyoto University; Dalian University of Technology; Hirosaki University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-007-0119-3
• 发表日期: 2009
• 页码: 343-368
• 关键词: linear complementarity constraints; sqp methods; CONVERGENCE; scheme

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.