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 a ttempts were made to prove polynomiality of other barrier methods (e.g . the inverse barrier method) but without success. Other interior poin t methods could be defined based on constant elasticity of substitutio n CES-functions. The classical inverse barrier function and the CES-fu nctions have a similar structure. In this paper, we compare the path d efined by the inverse barrier function and the path defined by CES-fun ctions in the case of linear programming. It will be shown that the tw o paths are equivalent, although parameterized differently. We also co nstruct a dual of the CES-function problem which is based on the dual CES-function. This result also completes the duality results for linea r programs with one CES-type (p-norm) type constraint.