On the complexity of finding first-order critical points in constrained nonlinear optimization

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

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Abstract

The complexity of finding e-Approximate first-order critical points for the general smooth constrained optimization problem is shown to be no worse that O(e-2) in terms of function and constraints evaluations. This result is obtained by analyzing the worst-case behaviour of a first-order short-step homotopy algorithm consisting of a feasibility phase followed by an optimization phase, and requires minimal assumptions on the objective function. Since a bound of the same order is known to be valid for the unconstrained case, this leads to the conclusion that the presence of possibly nonlinear/nonconvex inequality/equality constraints is irrelevant for this bound to apply. © 2012 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

Original languageEnglish
Pages (from-to)93-106
Number of pages14
JournalMathematical Programming
Volume144
Issue number1-2
DOIs
Publication statusPublished - 2014

Keywords

  • Constrained nonlinear optimization
  • Evaluation complexity
  • 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

    • 4 Oral presentation
    • 3 Research/Teaching in a external institution
    • 1 Participation in workshop, seminar, course
    • 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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