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Deterministic Bi-Criteria Model for Solving Stochastic Mixed Vector Variational Inequality Problems

Author

Listed:
  • Meiju Luo

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China)

  • Menghan Du

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China)

  • Yue Zhang

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China)

Abstract

In this paper, we consider stochastic mixed vector variational inequality problems. Firstly, we present an equivalent form for the stochastic mixed vector variational inequality problems. Secondly, we present a deterministic bi-criteria model for giving the reasonable resolution of the stochastic mixed vector variational inequality problems and further propose the approximation problem for solving the given deterministic model by employing the smoothing technique and the sample average approximation method. Thirdly, we obtain the convergence analysis for the proposed approximation problem while the sample space is compact. Finally, we propose a compact approximation method when the sample space is not a compact set and provide the corresponding convergence results.

Suggested Citation

  • Meiju Luo & Menghan Du & Yue Zhang, 2023. "Deterministic Bi-Criteria Model for Solving Stochastic Mixed Vector Variational Inequality Problems," Mathematics, MDPI, vol. 11(15), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3376-:d:1208826
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    References listed on IDEAS

    as
    1. Smith, Adam, 1977. "An Inquiry into the Nature and Causes of the Wealth of Nations," University of Chicago Press Economics Books, University of Chicago Press, number 9780226763743 edited by Cannan, Edwin.
    2. M. J. Luo & G. H. Lin, 2009. "Expected Residual Minimization Method for Stochastic Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 103-116, January.
    3. M. J. Luo & G. H. Lin, 2009. "Convergence Results of the ERM Method for Nonlinear Stochastic Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 569-581, September.
    4. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, July.
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