Activities per year
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 |
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Pages (from-to) | 359-368 |
Number of pages | 10 |
Journal | Mathematical Programming |
Volume | 163 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 15 Apr 2017 |
Keywords
- Evaluation complexity
- High-order models
- Nonlinear optimization
- Regularization
- Unconstrained optimization
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Activities
- 6 Invited talk
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Worst-case evaluation complexity for nonconvex optimization: adventures in the jungle of high-order nonlinear optimization
Philippe Toint (Speaker)
8 Sep 2018Activity: Talk or presentation types › Invited talk
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A path and some adventures in the jungle of high-order nonlinear optimization
Philippe Toint (Speaker)
24 Oct 2017Activity: Talk or presentation types › Invited talk
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A path and some adventures in the jungle of high-order nonlinear optimization
Philippe Toint (Speaker)
23 Oct 2017Activity: Talk or presentation types › Invited talk