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 defined based on constant elasticity of substitution (CES)-functions. 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 CES-functions 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 CES-function. This result also completes the duality results for linear programs with one CES-type (p-norm) type constraint.