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Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities

Author

Listed:
  • Yong Zhao

    (Sichuan University)

  • Jin Zhang

    (Hong Kong Baptist University)

  • Xinmin Yang

    (Chongqing Normal University)

  • Gui-Hua Lin

    (Shanghai University)

Abstract

This paper considers a class of vector variational inequalities. First, we present an equivalent formulation, which is a scalar variational inequality, for the deterministic vector variational inequality. Then we concentrate on the stochastic circumstance. By noting that the stochastic vector variational inequality may not have a solution feasible for all realizations of the random variable in general, for tractability, we employ the expected residual minimization approach, which aims at minimizing the expected residual of the so-called regularized gap function. We investigate the properties of the expected residual minimization problem, and furthermore, we propose a sample average approximation method for solving the expected residual minimization problem. Comprehensive convergence analysis for the approximation approach is established as well.

Suggested Citation

  • Yong Zhao & Jin Zhang & Xinmin Yang & Gui-Hua Lin, 2017. "Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 545-566, November.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:2:d:10.1007_s10957-016-0939-5
    DOI: 10.1007/s10957-016-0939-5
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    References listed on IDEAS

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    9. S. J. Li & Hong Yan & G. Y. Chen, 2003. "Differential and sensitivity properties of gap functions for vector variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 377-391, August.
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    Cited by:

    1. Elena Molho & Domenico Scopelliti, 2023. "On the study of multistage stochastic vector quasi-variational problems," Journal of Global Optimization, Springer, vol. 86(4), pages 931-952, August.

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