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Iterative Algorithm for Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities

Author

Listed:
  • L. C. Zeng

    (Shanghai Normal University)

  • S. Schaible

    (University of California)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

The auxiliary principle technique is extended to study the generalized strongly nonlinear mixed variational-like inequality problem for set-valued mappings without compact values. We establish first the existence of a solution of the related auxiliary problem. Then, the iterative algorithm for solving that problem is given by using this existence result. Moreover, the existence of a solution of the original problem and the convergence of iterative sequences generated by the algorithm are both derived.

Suggested Citation

  • L. C. Zeng & S. Schaible & J. C. Yao, 2005. "Iterative Algorithm for Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 725-738, March.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:3:d:10.1007_s10957-004-1182-z
    DOI: 10.1007/s10957-004-1182-z
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    References listed on IDEAS

    as
    1. Q. H. Ansari & J. C. Yao, 2001. "Iterative Schemes for Solving Mixed Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 527-541, March.
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    Cited by:

    1. S. Plubtieng & T. Thammathiwat, 2010. "A viscosity approximation method for equilibrium problems, fixed point problems of nonexpansive mappings and a general system of variational inequalities," Journal of Global Optimization, Springer, vol. 46(3), pages 447-464, March.
    2. X. Ding & Y. Liou & J. Yao, 2012. "Existence and algorithms for bilevel generalized mixed equilibrium problems in Banach spaces," Journal of Global Optimization, Springer, vol. 53(2), pages 331-346, June.
    3. L. Zeng & J. Yao, 2009. "A hybrid extragradient method for general variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 141-158, March.
    4. S. Schaible & J. C. Yao & L. C. Zeng, 2006. "Iterative Method for Set-Valued Mixed Quasi-variational Inequalities in a Banach Space," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 425-436, June.
    5. X. P. Ding, 2012. "Auxiliary Principle and Algorithm of Solutions for a New System of Generalized Mixed Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 796-809, December.
    6. Bin-Chao Deng & Tong Chen, 2013. "Strong Convergence Theorems for a Pair of Strictly Pseudononspreading Mappings," Journal of Mathematics, Hindawi, vol. 2013, pages 1-7, July.
    7. Lu-Chuan Ceng & Chang-yu Wang & Jen-Chih Yao, 2008. "Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(3), pages 375-390, June.
    8. Anchalee Sripattanet & Atid Kangtunyakarn, 2019. "Convergence Theorem of Two Sequences for Solving the Modified Generalized System of Variational Inequalities and Numerical Analysis," Mathematics, MDPI, vol. 7(10), pages 1-18, October.

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