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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    L. C. Ceng

  2. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China

    L. C. Ceng

  3. Department of Mathematics, University of Pisa, Largo B. Pontecorvo 5, 56127, Pisa, Italy

    G. Mastroeni

  4. Department of Applied Mathematics, National Sun Yat-sen University, 804, Kaohsiung, Taiwan

    J. C. Yao

Authors
  1. L. C. Ceng
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  2. G. Mastroeni
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  3. J. C. Yao
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Corresponding author

Correspondence to J. C. Yao.

Additional information

Communicated by F. Giannessi.

The research of L.C. Ceng was partially supported by the National Science Foundation of China (10771141), Ph.D. Program Foundation of Ministry of Education of China (20070270004), Science and Technology Commission of Shanghai Municipality Grant (075105118), Innovation Program of Shanghai Municipal Education Commission (09ZZ133), and Shanghai Leading Academic Discipline Project (S30405).

The research of J.C. Yao was partially supported by Grant NSC 97-2115-M-110-001.

Research was carried on within the agreement between National Sun Yat-Sen University of Kaohsiung, Taiwan and Pisa University, Pisa, Italy, 2008.

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Ceng, L.C., Mastroeni, G. & Yao, J.C. Hybrid Proximal-Point Methods for Common Solutions of Equilibrium Problems and Zeros of Maximal Monotone Operators. J Optim Theory Appl 142, 431–449 (2009). https://doi.org/10.1007/s10957-009-9538-z

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  • DOI: https://doi.org/10.1007/s10957-009-9538-z

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