Proximal point method for a special class of nonconvex functions on Hadamard manifolds

被引：61
作者：
Bento, G. C. [1 ]
Ferreira, O. P. [1 ]
Oliveira, P. R. [2 ]
机构：
[1] Univ Fed Goias, IME, BR-74001970 Goiania, Go, Brazil
[2] Univ Fed Rio de Janeiro, COPPE Sistemas, BR-21945970 Rio De Janeiro, RJ, Brazil
来源：
OPTIMIZATION | 2015年 / 64卷 / 02期
关键词：
Hadamard manifolds; nonconvex functions; proximal point method; 49M30; 90C26; STEEPEST DESCENT METHOD; MONOTONE VECTOR-FIELDS; NEWTONS METHOD; RIEMANNIAN-MANIFOLDS; VARIATIONAL-INEQUALITIES; NONSMOOTH ANALYSIS; LOCAL CONVERGENCE; CONVEX-FUNCTIONS; QUASI-CONVEX; SUBGRADIENT;
D O I：
10.1080/02331934.2012.745531
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：
In this article, we present the proximal point method for finding minima of a special class of nonconvex function on a Hadamard manifold. The well definedness of the sequence generated by the proximal point method is established. Moreover, it is proved that each accumulation point of this sequence satisfies the necessary optimality conditions and, under additional assumptions, its convergence for a minima is obtained.
引用
收藏
页码：289 / 319
页数：31
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