Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models

Ernesto Birgin, John Gardenghi, José-Mario Martinez, Sandra Augusta Santos, Philippe Toint

Research output: Working paper

55 Downloads (Pure)

Abstract

The worst-case evaluation complexity for smooth (possibly nonconvex) unconstrained optimization is considered. It is shown that, if one is willing to use derivatives of the objective function up to order $p$ (for $p\geq 1$) and to assume Lipschitz continuity of the $p$-th derivative, then an $\epsilon$-approximate first-order critical point can be computed in at most $O(\epsilon^{-(p+1)/p})$ evaluations of the problem's objective function and its derivatives. This generalizes and subsumes results known for $p=1$ and $p=2$.
Original languageEnglish
Place of Publication2015
PublisherNamur center for complex systems
Number of pages8
VolumenaXys-05-2015
Publication statusPublished - Jun 2015

Publication series

NamenaXys Technical Reports
PublishernaXys
Volume05-2015

Keywords

  • Nonlinear optimization
  • Complexity theory
  • High-order models

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  • Projects

    Complexity in nonlinear optimization

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

    1/11/08 → …

    Project: Research

    Activities

    • 4 Invited talk
    • 4 Oral presentation
    • 1 Research/Teaching in a external institution
    • 1 Visiting an external academic institution

    A path and some adventures in the jungle of high-order nonlinear optimization

    Philippe Toint (Speaker)

    23 Oct 2017

    Activity: Talk or presentation typesInvited talk

    A path and some adventures in the jungle of high-order nonlinear optimization

    Philippe Toint (Speaker)

    24 Oct 2017

    Activity: Talk or presentation typesInvited talk

    Cite this

    Birgin, E., Gardenghi, J., Martinez, J-M., Santos, S. A., & Toint, P. (2015). Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. (naXys Technical Reports; Vol. 05-2015). Namur center for complex systems.