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A Limited-Memory Multipoint Symmetric Secant Method for Bound Constrained Optimization

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Abstract

A new algorithm for solving smooth large-scale minimization problems with bound constraints is introduced. The way of dealing with active constraints is similar to the one used in some recently introduced quadratic solvers. A limited-memory multipoint symmetric secant method for approximating the Hessian is presented. Positive-definiteness of the Hessian approximation is not enforced. A combination of trust-region and conjugate-gradient approaches is used to explore useful information. Global convergence is proved for a general model algorithm. Results of numerical experiments are presented.

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Authors and Affiliations

  1. Division of Optimization, Department of Mathematics, Linköping University, S-581 83, Linköping, Sweden

    Oleg P. Burdakov

  2. Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970, Campinas SP, Brazil

    José Mario Martínez

  3. Facultad de Matemática, Astronomía y Física, FaMAF-CIEM, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000, Argentina

    Elvio A. Pilotta

Authors
  1. Oleg P. Burdakov
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  2. José Mario Martínez
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  3. Elvio A. Pilotta
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Burdakov, O.P., Martínez, J.M. & Pilotta, E.A. A Limited-Memory Multipoint Symmetric Secant Method for Bound Constrained Optimization. Annals of Operations Research 117, 51–70 (2002). https://doi.org/10.1023/A:1021561204463

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