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Dynamic smoothness parameter for fast gradient methods

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Abstract

We present and computationally evaluate a variant of the fast gradient method by Nesterov that is capable of exploiting information, even if approximate, about the optimal value of the problem. This information is available in some applications, among which the computation of bounds for hard integer programs. We show that dynamically changing the smoothness parameter of the algorithm using this information results in a better convergence profile of the algorithm in practice.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Pisa, Italy

    Antonio Frangioni

  2. Centre Interuniversitaire de Recherche sur les Réseaux d’Entreprise, la Logistique et le Transport (CIRRELT), Montreal, Canada

    Bernard Gendron

  3. Department of Computer Science and Operations Research, Université de Montréal, Montreal, Canada

    Bernard Gendron

  4. Indian Institute of Management Bangalore (IIMB), Bangalore, India

    Enrico Gorgone

  5. Dipartimento di Matematica e Informatica, Università di Cagliari, Cagliari, Italy

    Enrico Gorgone

Authors
  1. Antonio Frangioni
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  2. Bernard Gendron
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  3. Enrico Gorgone
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Correspondence to Enrico Gorgone.

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Frangioni, A., Gendron, B. & Gorgone, E. Dynamic smoothness parameter for fast gradient methods. Optim Lett 12, 43–53 (2018). https://doi.org/10.1007/s11590-017-1168-z

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  • DOI: https://doi.org/10.1007/s11590-017-1168-z

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