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Modified Proximal-Point Algorithm for Maximal Monotone Operators in Banach Spaces

Author

Listed:
  • L. Li

    (Northeast Normal University
    Harbin Normal University)

  • W. Song

    (Harbin Normal University)

Abstract

We introduce an iterative sequence for finding the solution to 0∈T(v), where T : E⇉E * is a maximal monotone operator in a smooth and uniformly convex Banach space E. This iterative procedure is a combination of iterative algorithms proposed by Kohsaka and Takahashi (Abstr. Appl. Anal. 3:239–249, 2004) and Kamamura, Kohsaka and Takahashi (Set-Valued Anal. 12:417–429, 2004). We prove a strong convergence theorem and a weak convergence theorem under different conditions respectively and give an estimate of the convergence rate of the algorithm. An application to minimization problems is given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:138:y:2008:i:1:d:10.1007_s10957-008-9370-x
    DOI: 10.1007/s10957-008-9370-x
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    Cited by:

    1. Vahid Dadashi & Mihai Postolache, 2017. "Hybrid Proximal Point Algorithm and Applications to Equilibrium Problems and Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 518-529, August.
    2. 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.

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