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Improving Complexity of Structured Convex Optimization Problems Using SelfConcordant Barriers
, 2001
"... The purpose of this paper is to provide improved complexity results for several classes of structured convex optimization problems using to the theory of selfconcordant functions developed in [11]. We describe the classical shortstep interiorpoint method and optimize its parameters in order to pr ..."
Abstract

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The purpose of this paper is to provide improved complexity results for several classes of structured convex optimization problems using to the theory of selfconcordant functions developed in [11]. We describe the classical shortstep interiorpoint method and optimize its parameters in order to provide the best possible iteration bound. We also discuss the necessity of introducing two parameters in the definition of selfconcordancy and which one is the best to fix. A lemma from [3] is improved, which allows us to review several classes of structured convex optimization problems and improve the corresponding complexity results.
SelfConcordant Functions in Structured Convex Optimization
, 2000
"... This paper provides a selfcontained introduction to the theory of selfconcordant functions [8] and applies it to several classes of structured convex optimization problems. We describe the classical shortstep interiorpoint method and optimize its parameters to provide its best possible iteration ..."
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This paper provides a selfcontained introduction to the theory of selfconcordant functions [8] and applies it to several classes of structured convex optimization problems. We describe the classical shortstep interiorpoint method and optimize its parameters to provide its best possible iteration bound. We also discuss the necessity of introducing two parameters in the definition of selfconcordancy, how they react to addition and scaling and which one is the best to fix. A lemma from [2] is improved and allows us to review several classes of structured convex optimization problems and evaluate their algorithmic complexity, using the selfconcordancy of the associated logarithmic barriers.