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Hybrid Proximal-Point Methods for Common Solutions of Equilibrium Problems and Zeros of Maximal Monotone Operators

Author

Listed:
  • L. C. Ceng

    (Shanghai Normal University
    Scientific Computing Key Laboratory of Shanghai Universities)

  • G. Mastroeni

    (University of Pisa)

  • J. C. Yao

    (National Sun Yat-sen University)

Abstract

The purpose of this paper is to introduce and study two hybrid proximal-point algorithms for finding a common element of the set of solutions of an equilibrium problem and the set of solutions to the equation 0∈Tx for a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space X. Strong and weak convergence results of these two hybrid proximal-point algorithms are established, respectively.

Suggested Citation

  • L. C. Ceng & G. Mastroeni & J. C. Yao, 2009. "Hybrid Proximal-Point Methods for Common Solutions of Equilibrium Problems and Zeros of Maximal Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 431-449, September.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:3:d:10.1007_s10957-009-9538-z
    DOI: 10.1007/s10957-009-9538-z
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    References listed on IDEAS

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    1. L. C. Zeng & J. C. Yao, 2007. "An Inexact Proximal-Type Algorithm in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 145-161, October.
    2. L. Li & W. Song, 2008. "Modified Proximal-Point Algorithm for Maximal Monotone Operators in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 45-64, July.
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    Cited by:

    1. X. P. Ding, 2010. "Auxiliary Principle and Algorithm for Mixed Equilibrium Problems and Bilevel Mixed Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 347-357, August.
    2. Xie Ding, 2012. "Existence and iterative algorithm of solutions for a class of bilevel generalized mixed equilibrium problems in Banach spaces," Journal of Global Optimization, Springer, vol. 53(3), pages 525-537, July.

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