A proximal point algorithm for DC fuctions on Hadamard manifolds

被引：23

作者：

Souza, J. C. O. ^{[1
,2
]}

Oliveira, P. R. ^{[1
]}

机构：

[1] Univ Fed Rio de Janeiro, COPPE Sistemas, BR-21945970 Rio De Janeiro, RJ, Brazil

[2] Univ Fed Piaui, CEAD, Teresina, PI, Brazil

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2015年 / 63卷 / 04期

关键词：

Nonconvex optimization; Proximal point algorithm; DC functions; Hadamard manifolds; VARIATIONAL-INEQUALITIES; RIEMANNIAN-MANIFOLDS; VECTOR-FIELDS; NEWTONS METHOD; MONOTONE; CONVERGENCE;

D O I：

10.1007/s10898-015-0282-7

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：

An extension of a proximal point algorithm for difference of two convex functions is presented in the context of Riemannian manifolds of nonposite sectional curvature. If the sequence generated by our algorithm is bounded it is proved that every cluster point is a critical point of the function (not necessarily convex) under consideration, even if minimizations are performed inexactly at each iteration. Application in maximization problems with constraints, within the framework of Hadamard manifolds is presented.

引用

页码：797 / 810

页数：14

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