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

E. G. Birgin; J. L. Gardenghi; J. M. Martínez; S. A. Santos; P. L. Toint

doi:10.1007/s10107-016-1065-8

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

E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos, P. L. Toint

Namur Institute for Complex Systems

Research output: Contribution to journal › Article

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≥ 1 ) and to assume Lipschitz continuity of the p-th derivative, then an ϵ-approximate first-order critical point can be computed in at most O(ϵ ^- ⁽ ^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 language	English
Pages (from-to)	359-368
Number of pages	10
Journal	Mathematical Programming
Volume	163
Issue number	1-2
DOIs	https://doi.org/10.1007/s10107-016-1065-8
Publication status	Published - 15 Apr 2017

Keywords

Evaluation complexity
High-order models
Nonlinear optimization
Regularization
Unconstrained optimization

Access to Document

10.1007/s10107-016-1065-8

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Activities

6 Invited talk

Worst-case evaluation complexity for nonconvex optimization: adventures in the jungle of high-order nonlinear optimization

Philippe Toint (Speaker)

8 Sep 2018

Activity: Talk or presentation types › Invited talk

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

Philippe Toint (Speaker)

23 Oct 2017

Activity: Talk or presentation types › Invited talk

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

Philippe Toint (Speaker)

24 Oct 2017

Activity: Talk or presentation types › Invited talk

Cite this

Birgin, E. G., Gardenghi, J. L., Martínez, J. M., Santos, S. A., & Toint, P. L. (2017). Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models. Mathematical Programming, 163(1-2), 359-368. https://doi.org/10.1007/s10107-016-1065-8

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