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Nonlinear Proximal Decomposition Method for Convex Programming

Author

Listed:
  • M. Kyono

    (Kyoto University)

  • M. Fukushima

    (Kyoto University)

Abstract

In this paper, we propose a new decomposition method for solving convex programming problems with separable structure. The proposed method is based on the decomposition method proposed by Chen and Teboulle and the nonlinear proximal point algorithm using the Bregman function. An advantage of the proposed method is that, by a suitable choice of the Bregman function, each subproblem becomes essentially the unconstrained minimization of a finite-valued convex function. Under appropriate assumptions, the method is globally convergent to a solution of the problem.

Suggested Citation

  • M. Kyono & M. Fukushima, 2000. "Nonlinear Proximal Decomposition Method for Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 357-372, August.
    • Handle: RePEc:spr:joptap:v:106:y:2000:i:2:d:10.1023_a:1004655531273
    DOI: 10.1023/A:1004655531273
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    References listed on IDEAS

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    1. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
    2. Jonathan Eckstein, 1993. "Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 202-226, February.
    3. Alfred Auslender & Marc Teboulle & Sami Ben-Tiba, 1999. "Interior Proximal and Multiplier Methods Based on Second Order Homogeneous Kernels," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 645-668, August.
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    Cited by:

    1. Ceng, Lu-Chuan & Yao, Jen-Chih, 2007. "Approximate proximal methods in vector optimization," European Journal of Operational Research, Elsevier, vol. 183(1), pages 1-19, November.
    2. L. C. Ceng & B. S. Mordukhovich & J. C. Yao, 2010. "Hybrid Approximate Proximal Method with Auxiliary Variational Inequality for Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 267-303, August.

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