Two simple proofs of analyticity of the central path in linear programming

Margareta Halicka

Several papers have appeared recently establishing the analyticity of the interior point paths at the boundary point for both linear programs and linear complementarity problems. While the proofs for LP are large, proceeding from limiting properties of the corresponding derivatives, the proofs for LCP are very simple, consisting in an application of the implicit function theorem to a certain system of equations. Inspired by the approach for LCP, this paper gives two simple ways of prooving the analyticity of the central path for LP. One follows the idea for LCP, the other consists in a proper partition of the system defining the central path.

Mathematics Preprint No. M198, Faculty of Mathematics and Physics, Comenius University, Bratislava, Slovakia