LINEAR CONVERGENCE OF SUBGRADIENT ALGORITHM FOR CONVEX FEASIBILITY ON RIEMANNIAN MANIFOLDS

被引：24

作者：

Wang, Xiangmei ^{[1
]}

Li, Chong ^{[2
]}

Wang, Jinhua ^{[3
]}

Yao, Jen-Chih ^{[4
]}

机构：

[1] Guizhou Univ, Coll Sci, Guiyang 550025, Peoples R China

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

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

[4] China Med Univ, Ctr Gen Educ, Taichung 40402, Taiwan

来源：

SIAM JOURNAL ON OPTIMIZATION | 2015年 / 25卷 / 04期

基金：

中国国家自然科学基金;

关键词：

convex feasibility problem; subgradient projection algorithm; Riemannian manifold; sectional curvature; linear convergence; finite termination; PROXIMAL POINT ALGORITHM; MONOTONE VECTOR-FIELDS; NEWTONS METHOD; VARIATIONAL-INEQUALITIES; ALTERNATING PROJECTIONS; SET;

D O I：

10.1137/14099961X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the convergence issue of the subgradient algorithm for solving the convex feasibility problems in Riemannian manifolds, which was first proposed and analyzed by Bento and Melo [J. Optim. Theory Appl., 152 (2012), pp. 773-785]. The linear convergence property about the subgradient algorithm for solving the convex feasibility problems with the Slater condition in Riemannian manifolds are established, and some step sizes rules are suggested for finite convergence purposes, which are motivated by the work due to De Pierro Iusem [Appl. Math. Optim., 17 (1988), pp. 225-235]. As a by-product, the convergence result of this algorithm is obtained for the convex feasibility problem without the Slater condition assumption. These results extend and/or improve the corresponding known ones in both the Euclidean space and Riemannian manifolds.

引用

页码：2334 / 2358

页数：25

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