Activities per year
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≥ 1 ) and to assume Lipschitz continuity of the pth derivative, then an ϵapproximate firstorder 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 (fromto)  359368 
Number of pages  10 
Journal  Mathematical Programming 
Volume  163 
Issue number  12 
DOIs  
Publication status  Published  15 Apr 2017 
Keywords
 Evaluation complexity
 Highorder models
 Nonlinear optimization
 Regularization
 Unconstrained optimization
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Activities
 6 Invited talk

Worstcase evaluation complexity for nonconvex optimization: adventures in the jungle of highorder nonlinear optimization
Philippe Toint (Speaker)
8 Sep 2018Activity: 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

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