A globally convergent primal-dual interior-point filter method for nonlinear programming

Michael Ulbrich (mulbrichmathematik.tu-muenchen.de)
Stefan Ulbrich (sulbrichmathematik.tu-muenchen.de)
Luis N. Vicente (lvicentemat.uc.pt)

Abstract: In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primal-dual interior-point algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, whose sizes are controlled by a trust-region type parameter. Each entry in the filter is a pair of coordinates: one resulting from feasibility and centrality, and associated with the normal step; the other resulting from optimality (complementarity and duality), and related with the tangential step. Global convergence to first-order critical points is proved for the new primal-dual interior-point filter algorithm.

Keywords: interior-point methods, primal-dual, filter, global convergence

Category 1: Nonlinear Optimization

Citation: Preprint 00-11 Department of Mathematics, University of Coimbra, Portugal April 2000, Revised February 2002

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Entry Submitted: 02/11/2002
Entry Accepted: 02/11/2002
Entry Last Modified: 02/11/2002

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