Proximal Methods in View of Interior-Point Strategies

A. Kaplan and R. Tichatschke
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A. Kaplan: Technical University of Darmstadt
R. Tichatschke: University of Trier

Journal of Optimization Theory and Applications, 1998, vol. 98, issue 2, No 7, 399-429

Abstract: 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.

Keywords: Interior-point methods; convex optimization; ill-posed problems; proximal point algorithms (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1022693618829

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