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

C. Cartis, N. I.M. Gould, Ph L. Toint

    Research output: Contribution to journalArticlepeer-review

    Abstract

    The complexity of finding ϵ ϵ -approximate first-order critical points for the general smooth constrained optimization problem is shown to be no worse that O(ϵ −2 ) O(ϵ−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.

    Original languageEnglish
    Pages (from-to)611-626
    Number of pages16
    JournalMathematical Programming
    Volume161
    Issue number1-2
    DOIs
    Publication statusPublished - 1 Jan 2017

    Keywords

    • Constrained nonlinear optimization
    • Evaluation complexity
    • Worst-case analysis

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