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International Journal of Bifurcation and Chaos (IJBC)

in Applied Sciences and Engineering

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Volume: 15, Issue: 3(2005) pp. 827-839 DOI: 10.1142/S0218127405012363
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Title:	NEWTON FLOW AND INTERIOR POINT METHODS IN LINEAR PROGRAMMING
Author(s):	JEAN-PIERRE DEDIEU MIP. Département de Mathématique, Université Paul Sabatier, 31062 Toulouse cedex 04, France MIKE SHUB Department of Mathematics, University of Toronto, 100 St. George Street, Toronto, Ontario M5S 3G3, Canada
History:	Received January 12, 2004 Revised June 17, 2004
Abstract:	We study the geometry of the central paths of linear programming theory. These paths are the solution curves of the Newton vector field of the logarithmic barrier function. This vector field extends to the boundary of the polytope and we study the main properties of this extension: continuity, analyticity, singularities.
Keywords:	Linear programming; interior point method; central path; Newton vector field; extension

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