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Stochastic Nonlinear Complementarity Problems: Stochastic Programming Reformulation and Penalty-Based Approximation Method

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  • M. Wang

    (Dalian University of Technology
    University of the Witwatersrand)

  • M. M. Ali

    (University of the Witwatersrand)

Abstract

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

Suggested Citation

  • M. Wang & M. M. Ali, 2010. "Stochastic Nonlinear Complementarity Problems: Stochastic Programming Reformulation and Penalty-Based Approximation Method," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 597-614, March.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:3:d:10.1007_s10957-009-9606-4
    DOI: 10.1007/s10957-009-9606-4
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1996. "Analysis of Sample-Path Optimization," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 513-528, August.
    2. Xiaojun Chen & Masao Fukushima, 2005. "Expected Residual Minimization Method for Stochastic Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 1022-1038, November.
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    4. C. Zhang & X. Chen, 2008. "Stochastic Nonlinear Complementarity Problem and Applications to Traffic Equilibrium under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 277-295, May.
    5. Huifu Xu & Fanwen Meng, 2007. "Convergence Analysis of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Equality Constraints," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 648-668, August.
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    Cited by:

    1. Liyan Xu & Bo Yu, 2014. "CVaR-constrained stochastic programming reformulation for stochastic nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 58(2), pages 483-501, June.

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