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CVaR-constrained stochastic programming reformulation for stochastic nonlinear complementarity problems

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  • Liyan Xu
  • Bo Yu

Abstract

We reformulate a stochastic nonlinear complementarity problem as a stochastic programming problem which minimizes an expected residual defined by a restricted NCP function with nonnegative constraints and CVaR constraints which guarantee the stochastic nonlinear function being nonnegative with a high probability. By applying smoothing technique and penalty method, we propose a penalized smoothing sample average approximation algorithm to solve the CVaR-constrained stochastic programming. We show that the optimal solution of the penalized smoothing sample average approximation problem converges to the solution of the corresponding nonsmooth CVaR-constrained stochastic programming problem almost surely. Finally, we report some preliminary numerical test results. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:58:y:2014:i:2:p:483-501
    DOI: 10.1007/s10589-013-9625-9
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    References listed on IDEAS

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    1. 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.
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