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

Gui Hua Lin; Xiaojun Chen; Masao Fukushima

doi:10.1007/s10107-007-0119-3

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

Gui Hua Lin, Xiaojun Chen, Masao Fukushima

Research output: Journal article publication › Journal article › Academic research › peer-review

44 Citations (Scopus)

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.

Original language	English
Pages (from-to)	343-368
Number of pages	26
Journal	Mathematical Programming
Volume	116
Issue number	1-2
DOIs	https://doi.org/10.1007/s10107-007-0119-3
Publication status	Published - 1 Jan 2009
Externally published	Yes

Keywords

Here-and-now
Quasi-Monte Carlo method
Smoothing implicit programming
Stochastic mathematical program with equilibrium constraints
Wait-and-see

ASJC Scopus subject areas

Applied Mathematics
General Mathematics
Safety, Risk, Reliability and Quality
Management Science and Operations Research
Software
Computer Graphics and Computer-Aided Design
General Computer Science

More information

10.1007/s10107-007-0119-3

Cite this

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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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AU - Fukushima, Masao

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N2 - 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.

AB - 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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KW - Quasi-Monte Carlo method

KW - Smoothing implicit programming

KW - Stochastic mathematical program with equilibrium constraints

KW - Wait-and-see

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

Abstract

Keywords

ASJC Scopus subject areas

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