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The deterministic ERM and CVaR reformulation for the stochastic generalized complementarity problem

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Abstract

In this paper, we consider the stochastic generalized complementarity problem (SGCP), which has a variety of important applications and has the stochastic complementarity problem as a special case. In order to give reasonable solutions of SGCP, we propose a deterministic formulation that minimizes the expected value of the residual function as the objective function and uses CVaR constraints to ensure the probabilistic feasibility of its solutions. The resulting model containsnon-smooth constraints and expected value functions both in the objective function and constraints. We present approximation problems for solving this model using smoothing and Monte-Carlo techniques. We prove two convergence results of the proposed approximation problems. One is to increase the sample size only, the other is to let smoothing parameter tend to zero as sample increase together. The effectiveness of the proposed approach was demonstrated using numerical examples.

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Authors and Affiliations

  1. School of Mathematics, Liaoning University, Liaoning, 110036, China

    Meiju Luo

  2. Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, 50011, USA

    Lizhi Wang

Authors
  1. Meiju Luo
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  2. Lizhi Wang
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Corresponding author

Correspondence to Meiju Luo.

Additional information

This work was supported in part by National Natural Science Foundation of China (No. 11501275) and Scientific Research Fund of Liaoning Provincial Education Department (No. L2015199).

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Cite this article

Luo, M., Wang, L. The deterministic ERM and CVaR reformulation for the stochastic generalized complementarity problem. Japan J. Indust. Appl. Math. 34, 321–333 (2017). https://doi.org/10.1007/s13160-017-0262-z

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  • DOI: https://doi.org/10.1007/s13160-017-0262-z

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