A class of stochastic mathematical programs with complementarity constraints: reformulations and algorithms

Gui-Hua Lin; Masao Fukushima

doi:10.3934/jimo.2005.1.99

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2005, Volume 1, Issue 1: 99-122. Doi: 10.3934/jimo.2005.1.99

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A class of stochastic mathematical programs with complementarity constraints: reformulations and algorithms

Gui-Hua Lin^1, and
Masao Fukushima^2,

1.
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024
2.
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501

Received: April 30, 2004

Revised: October 31, 2004

Published: December 2004

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Abstract

We consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs), in which all decisions are required to be made here-and-now, before a random event is observed. We show that this kind of SMPEC plays a very important role in practice. In order to develop effective algorithms, we first give some reformulations of the SMPEC and then, based on these reformulations, we propose a smoothed penalty approach for solving the problem. A comprehensive convergence theory is also included.

Keywords:

stochastic mathematical program with equilibrium constraints,
hereand- now decision problem,
stationarity,
subdifferential,
convergence.

Mathematics Subject Classification: 90C15, 90C30, 90C33.

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