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

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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

Contact: halicka@fmph.uniba.sk