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Inverse barriers and CES--functions in linear programming

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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.

Contact: t.terlaky@twi.tudelft.nl