A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function

Coralia Cartis, Nicholas I M Gould, Philippe L. Toint

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Abstract

This short note considers and resolves the apparent contradiction between known worst-case complexity results for first- and second-order methods for solving unconstrained smooth nonconvex optimization problems and a recent note by Jarre [On Nesterov's smooth Chebyshev-Rosenbrock function, Optim. Methods Softw. (2011)] implying a very large lower bound on the number of iterations required to reach the solution's neighbourhood for a specific problem with variable dimension.

Original languageEnglish
Pages (from-to)451-457
Number of pages7
JournalOptimization Methods and Software
Volume28
Issue number3
DOIs
Publication statusPublished - 1 Jun 2013

Keywords

  • evaluation complexity
  • nonconvex optimization
  • worst-case analysis

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  • Projects

    Complexity in nonlinear optimization

    TOINT, P., Gould, N. I. M. & Cartis, C.

    1/11/08 → …

    Project: Research

    Activities

    • 3 Oral presentation
    • 2 Research/Teaching in a external institution
    • 1 Visiting an external academic institution

    How much patience do you have? Issues in complexity for nonlinear optimization

    Philippe Toint (Invited speaker)

    5 Feb 2016

    Activity: Talk or presentation typesOral presentation

    How much patience do you have? Issues in complexity for nonlinear optimization

    Philippe Toint (Speaker)

    31 Jan 2016

    Activity: Talk or presentation typesOral presentation

    Polytechnic University of Hong Kong

    Philippe Toint (Visiting researcher)

    31 Jan 201614 Feb 2016

    Activity: Visiting an external institution typesResearch/Teaching in a external institution

    Prizes

    Leverhulme Fellow

    TOINT, Philippe (Recipient), Sep 2015

    Prize: Fellowship awarded competitively

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