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.  D. den Hertog, F. Jarre, C. Roos, and T. Terlaky, A sufficient condition for self-concordance with application to some classes of structured convex programming problems, Mathematical Programming, Series B 69 (1995), no. 1, 75--88.  Y. E. Nesterov and A. S. Nemirovsky, Interior-point polynomial methods in convex programming, SIAM Studies in Applied Mathematics, SIAM Publications, Philadelphia, 1994.
IMAGE0102, Service MATHRO, Facult▒ Polytechnique de Mons, Mons, Belgium, Aug/01, to appear in EJOR