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Subgradient Method with Entropic Projections for Convex Nondifferentiable Minimization

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  • K. C. Kiwiel

    (Systems Research Institute)

Abstract

We replace orthogonal projections in the Polyak subgradient method for nonnegatively constrained minimization with entropic projections, thus obtaining an interior-point subgradient method. Inexact entropic projections are quite cheap. Global convergence of the resulting method is established.

Suggested Citation

  • K. C. Kiwiel, 1998. "Subgradient Method with Entropic Projections for Convex Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 159-173, January.
    • Handle: RePEc:spr:joptap:v:96:y:1998:i:1:d:10.1023_a:1022671302532
    DOI: 10.1023/A:1022671302532
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    References listed on IDEAS

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    1. Larsson, Torbjorn & Patriksson, Michael & Stromberg, Ann-Brith, 1996. "Conditional subgradient optimization -- Theory and applications," European Journal of Operational Research, Elsevier, vol. 88(2), pages 382-403, January.
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    3. Alfredo N. Iusem & Marc Teboulle, 1995. "Convergence Rate Analysis of Nonquadratic Proximal Methods for Convex and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 657-677, August.
    4. Marc Teboulle, 1992. "Entropic Proximal Mappings with Applications to Nonlinear Programming," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 670-690, August.
    5. 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.
    6. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    7. Krzysztof C. Kiwiel, 1997. "Free-Steering Relaxation Methods for Problems with Strictly Convex Costs and Linear Constraints," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 326-349, May.
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    Cited by:

    1. Dirk Lorenz & Marc Pfetsch & Andreas Tillmann, 2014. "An infeasible-point subgradient method using adaptive approximate projections," Computational Optimization and Applications, Springer, vol. 57(2), pages 271-306, March.
    2. A. Auslender & M. Teboulle, 2004. "Interior Gradient and Epsilon-Subgradient Descent Methods for Constrained Convex Minimization," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 1-26, February.

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