Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization |
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Authors: | Gui-Hua Lin Xiaojun Chen Masao Fukushima |
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Institution: | 1. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, China 2. Department of Mathematical System Science, Hirosaki University, Hirosaki, 036-8560, Japan 3. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan
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Abstract: | 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. |
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