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Asymptotic Behavior of Continuous Trajectories for Primal-Dual Potential-Reduction Methods

Reha H Tutuncu (reha***at***cmu.edu)

Abstract: This article considers continuous trajectories of the vector fields induced by primal-dual potential-reduction algorithms for solving linear programming problems. It is known that these trajectories converge to the analytic center of the primal-dual optimal face. We establish that this convergence may be tangential to the central path, tangential to the optimal face, or in between, depending on the value of the potential function parameter.

Keywords: linear programming, potential functions, potential-reduction methods, central path, continuous trajectories for linear programming

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: Research Report 01-CNA-012, Department of Mathematical Sciences, Carnegie Mellon University, September 2001, revised March 2003.

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Entry Submitted: 04/09/2003
Entry Accepted: 04/09/2003
Entry Last Modified: 04/09/2003

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