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CVaR-constrained stochastic programming reformulation for stochastic nonlinear complementarity problems

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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.

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Acknowledgements

The research was supported by the National Natural Science Foundation of China (11171051, 91230103).

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning, 116025, China

    Liyan Xu & Bo Yu

  2. College of Science, Harbin Engineering University, Harbin, Heilongjiang, 150001, China

    Liyan Xu

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  1. Liyan Xu
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  2. Bo Yu
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Correspondence to Bo Yu.

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Xu, L., Yu, B. CVaR-constrained stochastic programming reformulation for stochastic nonlinear complementarity problems. Comput Optim Appl 58, 483–501 (2014). https://doi.org/10.1007/s10589-013-9625-9

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