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Abstract
The worstcase 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 firstorder 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 

Place of Publication  2015 
Publisher  Namur center for complex systems 
Number of pages  8 
Volume  naXys052015 
Publication status  Published  Jun 2015 
Publication series
Name  naXys Technical Reports 

Publisher  naXys 
Volume  052015 
Keywords
 Nonlinear optimization
 Complexity theory
 Highorder models
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Dive into the research topics of 'Worstcase evaluation complexity for unconstrained nonlinear optimization using highorder regularized models'. Together they form a unique fingerprint.Projects
 2 Active

Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Project: Research

Activities

A path and some adventures in the jungle of highorder nonlinear optimization
Philippe Toint (Speaker)
24 Oct 2017Activity: Talk or presentation types › Invited talk

A path and some adventures in the jungle of highorder nonlinear optimization
Philippe Toint (Speaker)
23 Oct 2017Activity: Talk or presentation types › Invited talk

Highorder optimality conditions in nonlinear optimization: necessary conditions and a conceptual approach of evaluation complexity
Philippe Toint (Speaker)
5 Aug 2016Activity: Talk or presentation types › Invited talk