Improved second-order evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
نویسندگان
چکیده
The unconstrained minimization of a sufficiently smooth objective function f(x) is considered, for which derivatives up to order p, p ≥ 2, are assumed to be available. An adaptive regularization algorithm is proposed that uses Taylor models of the objective of order p and that is guaranteed to find a firstand second-order critical point in at most O (
منابع مشابه
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 -approximate first-order critical point can be computed in at most O( −(p+1)/p) evaluations of the problem’s obj...
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عنوان ژورنال:
- CoRR
دوره abs/1708.04044 شماره
صفحات -
تاریخ انتشار 2017