Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2005-003 (May 17, 2005)

Solving Stochastic Mathematical Programs with Equilibrium Constraints via Approximation and Smoothing Implicit Programming with Penalization
by Gui-Hua Lin, Xiaojun Chen and Masao Fukushima

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In this paper, we consider the stochastic mathematical programs with equilibrium constraints, which includes 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.