Improving Complexity of Structured Convex Optimization Problems Using Self-Concordant Barriers
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Faculte Polytechnique De Mons
The purpose of this paper is to provide improved complexity results for several classes of structured convex optimization problems using to the theory of self-concordant functions developed in . We describe the classical short-step interior-point 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 self-concordancy and which one is the best to fix. A lemma from  is improved, which allows us to review several classes of structured convex optimization problems and improve the corresponding complexity results.