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Variational Inequalities Approaches to Minimization Problems with Constraints of Generalized Mixed Equilibria and Variational Inclusions

Author

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  • Lu-Chuan Ceng

    (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China)

  • Mihai Postolache

    (Center for General Education, China Medical University, Taichung 40402, Taiwan
    Romanian Academy, Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, 050711 Bucharest, Romania
    Department of Mathematics and Informatics, University “Politehnica” of Bucharest, 060042 Bucharest, Romania)

  • Ching-Feng Wen

    (Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, Taiwan)

  • Yonghong Yao

    (School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China
    The Key Laboratory of Intelligent Information and Data Processing of NingXia Province, North Minzu University, Yinchuan 750021, China)

Abstract

Multistep composite implicit and explicit extragradient-like schemes are presented for solving the minimization problem with the constraints of variational inclusions and generalized mixed equilibrium problems. Strong convergence results of introduced schemes are given under suitable control conditions.

Suggested Citation

  • Lu-Chuan Ceng & Mihai Postolache & Ching-Feng Wen & Yonghong Yao, 2019. "Variational Inequalities Approaches to Minimization Problems with Constraints of Generalized Mixed Equilibria and Variational Inclusions," Mathematics, MDPI, vol. 7(3), pages 1-20, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:270-:d:214466
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    References listed on IDEAS

    as
    1. H. K. Xu & T. H. Kim, 2003. "Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 185-201, October.
    2. Lu-Chuan Ceng & Suliman Al-Homidan, 2014. "Algorithms of Common Solutions for Generalized Mixed Equilibria, Variational Inclusions, and Constrained Convex Minimization," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-25, January.
    3. L. C. Zeng & J. C. Yao, 2006. "Modified Combined Relaxation Method for General Monotone Equilibrium Problems in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 469-483, December.
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    Cited by:

    1. Lu-Chuan Ceng & Meijuan Shang, 2019. "Generalized Mann Viscosity Implicit Rules for Solving Systems of Variational Inequalities with Constraints of Variational Inclusions and Fixed Point Problems," Mathematics, MDPI, vol. 7(10), pages 1-18, October.
    2. Lu-Chuan Ceng & Xiaolong Qin & Yekini Shehu & Jen-Chih Yao, 2019. "Mildly Inertial Subgradient Extragradient Method for Variational Inequalities Involving an Asymptotically Nonexpansive and Finitely Many Nonexpansive Mappings," Mathematics, MDPI, vol. 7(10), pages 1-19, September.

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