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A retrospective trust-region method for unconstrained optimization

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Abstract

We introduce a new trust-region method for unconstrained optimization where the radius update is computed using the model information at the current iterate rather than at the preceding one. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at last iterate. Global convergence to first- and second-order critical points is proved under classical assumptions and preliminary numerical experiments on CUTEr problems indicate that the new method is very competitive.

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Authors and Affiliations

  1. Computing Science and Operational Research Department, Université de Montréal, CP 6128, Succ. Centre-Ville, Montreal, QC, Canada

    Fabian Bastin

  2. Department of Mathematics, FUNDP, University of Namur, 61, Rue de Bruxelles, 5000, Namur, Belgium

    Vincent Malmedy, Philippe L. Toint & Dimitri Tomanos

  3. Fonds de la Recherche Scientifique, FNRS, 5, Rue d’Egmont, 1000, Brussels, Belgium

    Vincent Malmedy

  4. C.E.R.F.A.C.S., 42, Avenue Gustave Coriolis, 31057, Toulouse Cedex, France

    Mélodie Mouffe

  5. Fonds pour la formation à la Recherche dans l’Industrie et l’Agriculture, 5, Rue d’Egmont, 1000, Brussels, Belgium

    Dimitri Tomanos

Authors
  1. Fabian Bastin
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  2. Vincent Malmedy
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  3. Mélodie Mouffe
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  4. Philippe L. Toint
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  5. Dimitri Tomanos
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Correspondence to Fabian Bastin.

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Bastin, F., Malmedy, V., Mouffe, M. et al. A retrospective trust-region method for unconstrained optimization. Math. Program. 123, 395–418 (2010). https://doi.org/10.1007/s10107-008-0258-1

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  • DOI: https://doi.org/10.1007/s10107-008-0258-1

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