On the Existence and Convergence of the Central Path for Convex Programming and Some Duality Results

Authors:
Renato D. C. Monteiro;Fangjun Zou
Affiliations:
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332. E-mail: monteiro@isye.gatech.edu;School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332. E-mail: monteiro@isye.gatech.edu
Venue:
Computational Optimization and Applications
Year:
1998

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Abstract

This paper gives several equivalent conditions which guaranteethe existence of the weighted central paths for agiven convex programming problem satisfying some mild conditions.When the objective and constraint functions of the problem are analytic,we also characterize the limiting behavior of these pathsas they approach the set of optimal solutions.A duality relationship between a certain pair of logarithmic barrierproblems is also discussed.