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On the ERM formulation and a stochastic approximation algorithm of the stochastic- $$R_0$$ R 0 EVLCP

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  • Ming-Zheng Wang
  • M. Ali

Abstract

In this paper, a class of stochastic extended vertical linear complementarity problems is studied as an extension of the stochastic linear complementarity problem. The expected residual minimization (ERM) formulation of this stochastic extended vertical complementarity problem is proposed based on an NCP function. We study the corresponding properties of the ERM problem, such as existence of solutions, coercive property and differentiability. Finally, we propose a descent stochastic approximation method for solving this problem. A comprehensive convergence analysis is given. A number of test examples are constructed and the numerical results are presented. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Ming-Zheng Wang & M. Ali, 2014. "On the ERM formulation and a stochastic approximation algorithm of the stochastic- $$R_0$$ R 0 EVLCP," Annals of Operations Research, Springer, vol. 217(1), pages 513-534, June.
    • Handle: RePEc:spr:annopr:v:217:y:2014:i:1:p:513-534:10.1007/s10479-014-1575-9
    DOI: 10.1007/s10479-014-1575-9
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    References listed on IDEAS

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    1. 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.
    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. Gowda, M Seetharama & Sznajder, Roman, 1996. "A Generalization of the Nash Equilibrium Theorem on Bimatrix Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 1-12.
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