A note on inexact gradient and Hessian conditions for cubic regularized Newton's method

被引：5
|
作者：
Wang, Zhe [1 ]
Zhou, Yi [2 ]
Liang, Yingbin [1 ]
Lan, Guanghui [3 ]
机构：
[1] Ohio State Univ, Dept Elect & Comp Engn, Columbus, OH 43210 USA
[2] Duke Univ, Dept Elect & Comp Engn, Durham, NC 27708 USA
[3] Georgia Inst Technol, Dept Ind & Syst Engn, Atlanta, GA 30332 USA
来源：
OPERATIONS RESEARCH LETTERS | 2019年 / 47卷 / 02期
基金：
美国国家科学基金会;
关键词：
Nonconvex; Second-order methods; Second-order stationary points;
D O I：
10.1016/j.orl.2019.01.009
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
The inexact cubic-regularized Newton's method (CR) proposed by Cartis, Gould and Toint achieves the same convergence rate as exact CR proposed by Nesterov and Polyak, but the inexact condition is not implementable due to its dependence on a future variable. This note establishes the same convergence rate under a similar but implementable inexact condition, which depends on only current variables. Our proof bounds the function-value decrease over total iterations rather than each iteration in the previous studies. (C) 2019 Elsevier B.V. All rights reserved.
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页码：146 / 149
页数：4
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