A sufficient condition for self-concordance,with application to some classes of structured convex programming problems |
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Authors: | D den Hertog F Jarre C Roos T Terlaky |
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Institution: | (1) Faculty of Technical Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, Netherlands;(2) Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Am Hubland, Würzburg, Germany |
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Abstract: | Recently a number of papers were written that present low-complexity interior-point methods for different classes of convex programs. The goal of this article is to show that the logarithmic barrier function associated with these programs is self-concordant. Hence the polynomial complexity results for these convex programs can be derived from the theory of Nesterov and Nemirovsky on self-concordant barrier functions. We also show that the approach can be applied to some other known classes of convex programs.This author's research was supported by a research grant from SHELL.On leave from the Eötvös University, Budapest, Hungary. This author's research was partially supported by OTKA No. 2116. |
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Keywords: | Interior-point method Barrier function Dual geometric programming (Extended) entropy programming Primal and duall
p
-programming Relative Lipschitz condition Scaled Lipschitz condition Self-concordance |
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