: This paper is devoted to the study of a routing problem in telecommunication networks, when the cost function is the average delay. We establish asymptotic expansions for the value function and solutions in the vicinity of a congested nominal problem. The study is strongly related to the one of a partial inverse barrier method for linear programming. Key-words: Telecommunication networks, multicommodity flows, asymptotic expansions, linear programming, perturbation analysis, barrier functions, penalty methods. (R'esum'e : tsvp) INRIA, B.P. 105, 78153 Rocquencourt, France. Email: Frederic.Bonnans@inria.fr. y INRIA, B.P. 105, 78153 Rocquencourt, France. Email: Mounir.Haddou@inria.fr. Unité de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Téléphone : (33 1) 39 63 55 11 -- Télécopie : (33 1) 39 63 53 Analyse asymptotique des r'eseaux de communications congestionn'es R'esum'e : Nous 'etudions le probl`eme de minimisation d...

Recently much attention was paid to polynomial interior point methods, almost exclusively based on the logarithmic barrier function. Some attempts were made to prove polynomiality of other barrier methods (e.g. the inverse barrier method) but without success. Other interior point methods could be defined based on CES-functions (CES is the abbreviation of Constant Elasticity of Substitution). The classical inverse barrier function and the CES-functions have a similar structure. In this paper we compare the path defined by the inverse barrier function and the path defined by CESfunctions in the case of linear programming. It will be shown that the two paths are equivalent, although parameterized differently. We also construct a dual of the CES-function problem which is based on the dual CESfunction. This result also completes the duality results for linear programs with one CES-type (p-norm) type constraint. Key words: linear programming, interior-point methods, inverse barrier, CES-func...

. In this paper a duality of transformation functions in the interior point method is treated. A dual pair of convex or linear programming problems is considered and the primal problem is transformed by the parametrized transformation function of a more general form than logarithmic is. The construction of the parametrized transformation function for the dual problem is carried out so that both transformation functions were dual. The result obtained explains the unlucid construction of dual transformation functions so far known as a special case of a simple general principle of constructing dual transformation functions. 1. Introduction In the framework of the interior point methods (IPM) the linear programming problem (LP) min \Phi c T x j Ax = b; x 0 \Psi ; x; c 2 R n ; b 2 R m ; A 2 R m\Thetan is solved using logarithmic transformation function (1) T (x; ¯) = c T x \Gamma ¯ n X i=1 ln x i where x 2 P o = fx j Ax = b; x ? 0g and ¯ ? 0 is a parameter. The standard...

(will be inserted by the editor) A Majorize-Minimize line search algorithm for barrier functions