Finite Termination of Inexact Proximal Point Algorithms in Hilbert Spaces

被引：4

作者：

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

Li, C. ^{[2
]}

Yao, J. -C. ^{[3
,4
]}

机构：

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

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

[3] Kaohsiung Med Univ, Ctr Fundamental Sci, Kaohsiung 80702, Taiwan

[4] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2015年 / 166卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Finite termination; Inexact proximal point algorithms; Maximal monotone; Projected gradient method; WEAK SHARP MINIMA; VARIATIONAL INEQUALITY PROBLEM; MAXIMAL MONOTONE-OPERATORS; ERROR-BOUNDS; CONVERGENCE ANALYSIS; CONVEX-OPTIMIZATION; BANACH-SPACES; FIXED-POINTS; INCLUSIONS; PROGRAMS;

D O I：

10.1007/s10957-014-0689-1

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 the present paper, we study the finite termination of sequences generated by inexact proximal point algorithms for finding zeroes of a maximal monotone (set-valued) operator on a Hilbert space. Under some mild conditions, we get that a sequence generated by inexact proximal point algorithm stops after a finite number of iterations. Our results extend the corresponding results in Rockafellar (SIAM J Control Optim 14:877-898, 1976). In particular, for optimization problems, our results improve corresponding results in Ferris (Math Progr 50:359-366, 1991). As applications, we obtain finite termination of projected gradient method.

引用

页码：188 / 212

页数：25

共 50 条

[31] On the diagonal proximal point algorithms [J].

Khatibzadeh, Hadi ;

Rahimi Piranfar, Mohsen ;

Rooin, Jamal .

OPTIMIZATION, 2025, 74 (03) :655-682

[32] An inexact interior point proximal method for the variational inequality problem [J].

Burachik, Regina S. ;

Lopes, Jurandir O. ;

Da Silva, Geci J. P. .

COMPUTATIONAL & APPLIED MATHEMATICS, 2009, 28 (01) :15-36

[33] PROXIMAL POINT ALGORITHMS AND FOUR RESOLVENTS OF NONLINEAR OPERATORS OF MONOTONE TYPE IN BANACH SPACES [J].

Takahashi, Wataru .

TAIWANESE JOURNAL OF MATHEMATICS, 2008, 12 (08) :1883-1910

[34] Some unified algorithms for finding minimum norm fixed point of nonexpansive semigroups in Hilbert spaces [J].

Yao, Yonghong ;

Liou, Yeong-Cheng .

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2011, 19 (01) :331-346

[35] Hybrid Inertial Contraction Algorithms for Solving Variational Inequalities with Fixed Point Constraints in Hilbert Spaces [J].

Pham Ngoc Anh .

Acta Mathematica Vietnamica, 2022, 47 :743-753

[36] Hybrid Inertial Contraction Algorithms for Solving Variational Inequalities with Fixed Point Constraints in Hilbert Spaces [J].

Pham Ngoc Anh .

ACTA MATHEMATICA VIETNAMICA, 2022, 47 (04) :743-753

[37] Algorithms for approximating minimization problems in Hilbert spaces [J].

Yao, Yonghong ;

Kang, Shin Min ;

Liou, Yeong-Cheng .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (12) :3515-3526

[38] ALGORITHMS CONSTRUCTION FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES [J].

Li, Mengqin ;

Yao, Yonghong ;

Liou, Yeong-Cheng ;

Kang, Shin Min .

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2010, 11 (01) :35-43

[39] Strong Convergence of Two Iterative Algorithms for Nonexpansive Mappings in Hilbert Spaces [J].

Yao, Yonghong ;

Liou, Yeong Cheng ;

Marino, Giuseppe .

FIXED POINT THEORY AND APPLICATIONS, 2009,

[40] Proximal type algorithms involving linesearch and inertial technique for split variational inclusion problem in hilbert spaces with applications [J].

Kesornprom, Suparat ;

Cholamjiak, Prasit .

OPTIMIZATION, 2019, 68 (12) :2365-2391

← 1 2 3 4 5 →