Monotone and Accretive Vector Fields on Riemannian Manifolds

被引：91

作者：

Wang, J. H. ^{[1
]}

Lopez, G. ^{[2
]}

Martin-Marquez, V. ^{[2
]}

Li, C. ^{[3
,4
]}

机构：

[1] Zhejiang Univ Technol, Dept Appl Math, Hangzhou 310032, Zhejiang, Peoples R China

[2] Univ Seville, Dept Anal Matemat, E-41080 Seville, Spain

[3] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China

[4] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2010年 / 146卷 / 03期

关键词：

Hadamard manifold; Monotone vector field; Accretive vector field; Singularity; Fixed point; Iterative algorithm; Convex function; PROXIMAL POINT ALGORITHM; NEWTONS METHOD; NONSMOOTH ANALYSIS; CONVERGENCE; UNIQUENESS; EXISTENCE; OPERATORS; MAPPINGS;

D O I：

10.1007/s10957-010-9688-z

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 relationship between monotonicity and accretivity on Riemannian manifolds is studied in this paper and both concepts are proved to be equivalent in Hadamard manifolds. As a consequence an iterative method is obtained for approximating singularities of Lipschitz continuous, strongly monotone mappings. We also establish the equivalence between the strong convexity of functions and the strong monotonicity of its subdifferentials on Riemannian manifolds. These results are then applied to solve the minimization of convex functions on Riemannian manifolds.

引用

页码：691 / 708

页数：18

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