Computational Optimization and Applications

, Volume 58, Issue 2, pp 483–501 | Cite as

CVaR-constrained stochastic programming reformulation for stochastic nonlinear complementarity problems

Article

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.

Keywords

Stochastic complementarity problems Sample average approximation CVaR Penalized smoothing method R0 function 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianChina
  2. 2.College of ScienceHarbin Engineering UniversityHarbinChina

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