Inverse barriers and CES-functions in linear programming

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 de ned 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 de ned by the inverse barrier function and the path de ned by CESfunctions in the case of linear programming. It will be shown that the two paths are equivalent, although parameterized di erently. 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.