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Combined Monte Carlo sampling and penalty method for Stochastic nonlinear complementarity problems

Author: Gui-Hua Lin
Journal: Math. Comp. 78 (2009), 1671-1686
MSC (2000): Primary 90C33; Secondary 90C30, 90C15.
Published electronically: January 21, 2009
MathSciNet review: 2501069
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Abstract: In this paper, we consider a new formulation with recourse for a class of stochastic nonlinear complementarity problems. We show that the new formulation is equivalent to a smooth semi-infinite program that no longer contains recourse variables. We then propose a combined Monte Carlo sampling and penalty method for solving the problem in which the underlying sample space is assumed to be compact. Furthermore, we suggest a compact approximation approach for the case where the sample space is unbounded. Two preliminary numerical examples are included as well.

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Additional Information

Gui-Hua Lin
Affiliation: Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China

Keywords: Stochastic nonlinear complementarity problem, recourse, Monte Carlo method, penalization, convergence
Received by editor(s): May 14, 2007
Received by editor(s) in revised form: January 26, 2008, and July 13, 2008
Published electronically: January 21, 2009
Additional Notes: This work was supported in part by NSFC Grant #10771025 and SRFDP Grant #20070141063.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.