Inverse barriers and CES--functions in linear programming

H. van Maaren, T. Terlaky

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). These CES-functions come from the economics and they are used among others in production theory.

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 parametrized differently.

We also construct a dual of the CES-function problem which is based on the dual CES-function.

Report 95-76, Faculty of Technical Mathematics and Computer Science, Delft University of Technology, Delft, 1995.