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Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
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Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
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Journal Article
Worst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
2017
Overview
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
.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V
