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

Authors:
Michael Ulbrich;Stefan Ulbrich;Luís N. Vicente
Affiliations:
Fachbereich Mathematik, Schwerpunkt Optimierung und Approximation, Germany;Technische Universität München, Zentrum Mathematik M1, Germany;Universidade de Coimbra, Departamento de Matemática, Portugal
Venue:
Mathematical Programming: Series A and B
Year:
2004

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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.