A STRONGLY CONVERGENT METHOD FOR NONSMOOTH CONVEX MINIMIZATION IN HILBERT SPACES

被引：19

作者：

Bello Cruz, J. Y. ^{[1
]}

Iusem, A. N. ^{[2
]}

机构：

[1] Univ Fed Goias, Inst Matemat & Estat, BR-74001970 Goiania, Go, Brazil

[2] Jardim Bot, Inst Matemat Pura & Aplicada, Rio De Janeiro, Brazil

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2011年 / 32卷 / 10期

关键词：

Convex minimization; Nonsmooth optimization; Projected subgradient algorithm; Projection method; Strong convergence; MESH-INDEPENDENCE PRINCIPLE; IMAGE-RECONSTRUCTION; OPTIMIZATION;

D O I：

10.1080/01630563.2011.590914

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we propose a strongly convergent variant on the projected subgradient method for constrained convex minimization problems in Hilbert spaces. The advantage of the proposed method is that it converges strongly when the problem has solutions, without additional assumptions. The method also has the following desirable property: the sequence converges to the solution of the problem which lies closest to the initial iterate.

引用

页码：1009 / 1018

页数：10

共 50 条

[41] On the global convergence of a nonmonotone proximal bundle method for convex nonsmooth minimization
Hou, Liusheng
Sun, Wenyu
OPTIMIZATION METHODS & SOFTWARE, 2008, 23 (02): : 227 - 235
[42] Strongly Convergent Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces
Akashi, Shigeo
Kimura, Yasunori
Takahashi, Wataru
JOURNAL OF CONVEX ANALYSIS, 2015, 22 (04) : 917 - 938
[43] A strongly convergent hybrid proximal method in Banach spaces
Otero, RG
Svaiter, BF
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 289 (02) : 700 - 711
[44] VERY STRONGLY AND VERY WEAKLY CONVERGENT SEQUENCES IN LOCALLY CONVEX-SPACES
SIMOES, MA
PROCEEDINGS OF THE ROYAL IRISH ACADEMY SECTION A-MATHEMATICAL AND PHYSICAL SCIENCES, 1984, 84 (02) : 125 - 132
[45] A globally convergent proximal Newton-type method in nonsmooth convex optimization
Mordukhovich, Boris S.
Yuan, Xiaoming
Zeng, Shangzhi
Zhang, Jin
MATHEMATICAL PROGRAMMING, 2023, 198 (01) : 899 - 936
[46] A globally convergent proximal Newton-type method in nonsmooth convex optimization
Boris S. Mordukhovich
Xiaoming Yuan
Shangzhi Zeng
Jin Zhang
Mathematical Programming, 2023, 198 : 899 - 936
[47] On convergence of inexact projection gradient method for strongly convex minimization
Necoara, Ion
Patrascu, Andrei
Clipici, Dragos
Barbu, Marian
2017 21ST INTERNATIONAL CONFERENCE ON SYSTEM THEORY, CONTROL AND COMPUTING (ICSTCC), 2017, : 506 - 511
[48] DESCENT METHODS FOR NONSMOOTH CONVEX CONSTRAINED MINIMIZATION
KIWIEL, KC
LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS, 1985, 255 : 203 - 214
[49] Excessive gap technique in nonsmooth convex minimization
Nesterov, Y
SIAM JOURNAL ON OPTIMIZATION, 2005, 16 (01) : 235 - 249
[50] Synchronous Parallel Block Coordinate Descent Method for Nonsmooth Convex Function Minimization
Yutong Dai
Yang Weng
Journal of Systems Science and Complexity, 2020, 33 : 345 - 365

← 1 2 3 4 5 →