Convergence of interior point algorithms for the monotone linear complementarity problem

Convergence of interior point algorithms for the monotone linear complementarity problem

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Article ID: iaor20041821
Country: United States
Volume: 21
Issue: 1
Start Page Number: 1
End Page Number: 25
Publication Date: Feb 1996
Journal: Mathematics of Operations Research
Authors: ,
Keywords: complementarity, interior point methods, duality
Abstract:

The literature on interior point algorithms shows impressive results related to the speed of convergence of the objective values, but very little is known about the convergence of the iterate sequences. This paper studies the horizontal linear complementarity problem, and derives general convergence properties for algorithms based on Newton iterations. This problem provides a simple and general framework for most existing primal–dual interior point methods. The conclusion is that most of the published algorithms of this kind generate convergent sequences. In many cases (whenever the convergence is not too fast in a certain sense), the sequences converge to the analytic center of the optimal face.

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