Journal
MATHEMATICAL PROGRAMMING
Volume 163, Issue 1-2, Pages 359-368Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-016-1065-8
Keywords
Nonlinear optimization; Unconstrained optimization; Evaluation complexity; High-order models; Regularization
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Funding
- Brazilian agency FAPESP [2010/10133-0, 2013/03447-6, 2013/05475-7, 2013/07375-0, 2013/23494-9]
- Brazilian agency CNPq [304032/2010-7, 309517/2014-1, 303750/2014-6, 490326/2013-7]
- Belgian Fund for Scientific Research (FNRS)
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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 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.
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