Penalty-based SAA method of stochastic nonlinearcomplementarity problems

Ming-Zheng Wang; M. Montaz Ali

doi:10.3934/jimo.2010.6.241

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2010, Volume 6, Issue 1: 241-257. Doi: 10.3934/jimo.2010.6.241

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Penalty-based SAA method of stochastic nonlinear complementarity problems

Ming-Zheng Wang^1, and
M. Montaz Ali^2,

1.
School of Management, Dalian University of Technology, Dalian 116024, Liaoning Province
2.
School of Computational and Applied Mathematics, University of the Witwatersrand, Wits-2050, Johannesburg

Received: September 30, 2008

Revised: September 30, 2009

Published: December 2009

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Abstract

We consider a class of stochastic nonlinear complementarity problems. We first formulate the stochastic complementarity problem as a stochastic programming model. Based on this reformulation, we propose a penalty-based sample average approximation (in short, SAA) method for stochastic complementarity problem and prove its convergence. Finally, we report some numerical test results to show the efficiency of our method.

Keywords:

Stochastic nonlinear complementarity problems,
stochastic programming,
sample average approximation,
penalty method,
convergence.

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

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