2009Journal of Industrial and Management OptimizationRequires access

Penalty-based SAA method of stochastic nonlinear complementarity problems

Mingzheng Wang, M. Montaz Ali

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Abstract

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

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What this paper is about

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

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Available abstract

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

Key concepts: Mixed complementarity problem, Complementarity (molecular biology), Nonlinear complementarity problem, Mathematical optimization, Complementarity theory, Nonlinear system, Convergence (economics), Computer science

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