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

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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.

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Authors and Affiliations

  1. Schwerpunkt Optimierung und Approximation, Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, D-20146, Hamburg, Germany

    Michael Ulbrich

  2. Zentrum Mathematik M1, Technische Universität München, Boltzmannstr. 3, 85747, Garching b. München, Germany

    Stefan Ulbrich

  3. Departamento de Matemática, Universidade de Coimbra, 3001-454, Coimbra, Portugal

    Luís N. Vicente

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  1. Michael Ulbrich
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  2. Stefan Ulbrich
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Correspondence to Michael Ulbrich.

Additional information

Mathematics Subject Classification (1991): 65K05, 90C06, 90C29, 90C30

Support for this author was provided by CRPC grant CCR–9120008.

Support for this author was provided by CRPC grant CCR–9120008.

Support for this author was provided by Centro de Matemática da Universidade de Coimbra, by FCT under grant POCTI/35059/MAT/2000, by the European Union under grant IST-2000-26063, and by Fundaç\ ao Calouste Gulbenkian. The author would also like to thank the IBM T.J. Watson Research Center and the Institute for Mathematics and Its Applications for their local support.

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Ulbrich, M., Ulbrich, S. & Vicente, L. A globally convergent primal-dual interior-point filter method for nonlinear programming. Math. Program., Ser. A 100, 379–410 (2004). https://doi.org/10.1007/s10107-003-0477-4

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  • DOI: https://doi.org/10.1007/s10107-003-0477-4

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