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

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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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Authors and Affiliations

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, China

    Gui-Hua Lin

  2. Department of Mathematical System Science, Hirosaki University, Hirosaki, 036-8560, Japan

    Xiaojun Chen

  3. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Masao Fukushima

Authors
  1. Gui-Hua Lin
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  2. Xiaojun Chen
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  3. Masao Fukushima
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Corresponding author

Correspondence to Masao Fukushima.

Additional information

This paper is dedicated to Professor Alfred Auslender on the occasion of his 65th birthday.

This work was supported in part by the Scientific Research Grant-in-Aid from Japan Society for the Promotion of Science.

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Lin, GH., Chen, X. & Fukushima, M. Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization. Math. Program. 116, 343–368 (2009). https://doi.org/10.1007/s10107-007-0119-3

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  • DOI: https://doi.org/10.1007/s10107-007-0119-3

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