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Weighted Method for Uncertain Nonlinear Variational Inequality Problems

Author

Listed:
  • Cunlin Li

    (Ningxia Key Laboratory of Intelligent Information and Big Data Processing, Governance and Social Management Research Center of Northwest Ethnic Regions, North Minzu University, Yinchuan 750021, China
    State Key Laboratory of Mechanics Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
    School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
    These authors contributed equally to this work.)

  • Mihai Postolache

    (Center for General Education, China Medical University, Taichung 40402, Taiwan
    Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania
    Department of Mathematics and Informatics, University “Politehnica” of Bucharest, 060042 Bucharest, Romania
    These authors contributed equally to this work.)

  • Zhifu Jia

    (State Key Laboratory of Mechanics Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
    School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
    These authors contributed equally to this work.)

Abstract

A convex combined expectations regularized gap function with uncertain variable is presented to deal with uncertain nonlinear variational inequality problems (UNVIP). The UNVIP is transformed into a minimization problem through an uncertain weighted expected residual function. Moreover, the convergence of the global optimal solutions of the uncertain weighted expected residual minimization model is given through the integration by parts method under the compact space of the uncertain event. The limiting behaviors of the transformed model are analyzed. Furthermore, a compact approximation method is proposed in the unbounded uncertain event space. Through analysis of the convergence of UWERM model and reasonable hypothesis, the compact approximation method is verified under the circumstance of Holder continuity.

Suggested Citation

  • Cunlin Li & Mihai Postolache & Zhifu Jia, 2019. "Weighted Method for Uncertain Nonlinear Variational Inequality Problems," Mathematics, MDPI, vol. 7(10), pages 1-22, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:974-:d:276637
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    References listed on IDEAS

    as
    1. X.Q. Yang & J.C. Yao, 2002. "Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 407-417, November.
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