Penalty-based SAA method of stochastic nonlinear complementarity problems

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January 2010, 6(1): 241-257. doi: 10.3934/jimo.2010.6.241

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, China
2.	School of Computational and Applied Mathematics, University of the Witwatersrand, Wits-2050, Johannesburg, South Africa

Received October 2008 Revised October 2009 Published November 2009

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

Mathematics Subject Classification: 90C33, 90C30, 90C1.

Citation: Ming-Zheng Wang, M. Montaz Ali. Penalty-based SAA method of stochastic nonlinear complementarity problems. Journal of Industrial & Management Optimization, 2010, 6 (1) : 241-257. doi: 10.3934/jimo.2010.6.241

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