Projects 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 $p\geq 1$) 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 language | English |
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Place of Publication | 2015 |
Publisher | Namur center for complex systems |
Number of pages | 8 |
Volume | naXys-05-2015 |
Publication status | Published - Jun 2015 |
Publication series
Name | naXys Technical Reports |
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Publisher | naXys |
Volume | 05-2015 |
Keywords
- Nonlinear optimization
- Complexity theory
- High-order models
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Projects
- 2 Active
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Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Project: Research
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Activities
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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
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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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High-order optimality conditions in nonlinear optimization: necessary conditions and a conceptual approach of evaluation complexity
Philippe Toint (Speaker)
10 Aug 2016Activity: Talk or presentation types › Invited talk