Proximal Methods in View of Interior-Point Strategies |
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Authors: | Kaplan A. Tichatschke R. |
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Affiliation: | (1) Department of Mathematics, Technical University of Darmstadt, Darmstadt, Germany;(2) Department IV (Mathematics), University of Trier, Trier, Germany |
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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. |
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Keywords: | Interior-point methods convex optimization ill-posed problems proximal point algorithms |
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