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Proximal Methods in View of Interior-Point Strategies

Author

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  • A. Kaplan

    (Technical University of Darmstadt)

  • R. Tichatschke

    (University of Trier)

Abstract

This paper deals with regularized penalty-barrier methods for convex programming problems. In the spirit of an iterative proximal regularization approach, an interior-point method is constructed, in which at each step a strongly convex function has to be minimized and the prox-term can be scaled by a variable scaling factor. The convergence of the method is studied for an axiomatically given class of barrier functions. According to the results, a wide class of barrier functions (in particular, logarithmic and exponential functions) can be applied to design special algorithms. For the method with a logarithmic barrier, the rate of convergence is investigated and assumptions that ensure linear convergence are given.

Suggested Citation

  • A. Kaplan & R. Tichatschke, 1998. "Proximal Methods in View of Interior-Point Strategies," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 399-429, August.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:2:d:10.1023_a:1022693618829
    DOI: 10.1023/A:1022693618829
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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.
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    Cited by:

    1. Felipe Alvarez & Miguel Carrasco & Karine Pichard, 2005. "Convergence of a Hybrid Projection-Proximal Point Algorithm Coupled with Approximation Methods in Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 966-984, November.
    2. Felipe Alvarez & Miguel Carrasco & Thierry Champion, 2012. "Dual Convergence for Penalty Algorithms in Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 388-407, May.

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