Local analysis of the feasible primal–dual interior-point method

Local analysis of the feasible primal–dual interior-point method

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Article ID: iaor20091392
Country: Netherlands
Volume: 40
Issue: 1
Start Page Number: 41
End Page Number: 57
Publication Date: May 2008
Journal: Computational Optimization and Applications
Authors: , ,
Keywords: duality, interior point methods
Abstract:

In this paper we analyze the rate of local convergence of the Newton primal–dual interior-point method when the iterates are kept strictly feasible with respect to the inequality constraints. It is shown under the classical conditions that the rate is q-quadratic when the functions associated to the binding inequality constraints are concave. In general, the q-quadratic rate is achieved provided the step in the primal variables does not become asymptotically orthogonal to any of the gradients of the binding inequality constraints.

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