Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
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 -approximat...
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| Veröffentlicht in: | Mathematical programming Jg. 163; H. 1-2; S. 359 - 368 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.05.2017
Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 0025-5610, 1436-4646 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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
. |
|---|---|
| Bibliographie: | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0025-5610 1436-4646 |
| DOI: | 10.1007/s10107-016-1065-8 |