Local Analysis of the Feasible Primal-Dual Interior-Point Method

R. Silva (renatamat.uc.pt)
J. Soares (jsoaresmat.uc.pt)
L. N. Vicente (lnvmat.uc.pt)

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 inequality constraints define a locally concave feasible region. In the nonconcave case, 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.

Keywords: interior-point methods, strict feasibility, centrality, local convergence

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

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Entry Submitted: 03/18/2005
Entry Accepted: 03/18/2005
Entry Last Modified: 03/18/2005

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