PROXIMAL POINT METHODS FOR MONOTONE OPERATORS IN BANACH SPACES

被引：17
作者：
Aoyama, Koji [1 ]
Kohsaka, Fumiaki [2 ]
Takahashi, Wataru [3 ]
机构：
[1] Chiba Univ, Dept Econ, Chiba 2638522, Japan
[2] Oita Univ, Dept Comp Sci & Intelligent Syst, Oita 8701192, Japan
[3] Tokyo Inst Technol, Dept Math & Comp Sci, Meguro Ku, Tokyo 1528552, Japan
来源：
TAIWANESE JOURNAL OF MATHEMATICS | 2011年 / 15卷 / 01期
关键词：
Convex function; Firmly nonexpansive-type mapping; Fixed point; Minimization; Monotone operator; Proximal point algorithm; Uniformly convex Banach space; Zero point; RELATIVELY NONEXPANSIVE-MAPPINGS; STRONG-CONVERGENCE THEOREMS; FIXED-POINTS; WEAK; APPROXIMATION; ALGORITHM; FAMILY;
D O I：
10.11650/twjm/1500406174
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Some fundamental properties of resolvents of monotone operators in Banach spaces are investigated. Using them, we study the asymptotic behavior of the sequences generated by two modifications of the proximal point algorithm for monotone operators satisfying a range condition defined in Banach spaces.
引用
收藏
页码：259 / 281
页数：23
相关论文
共 42 条
[1]  
Alber Y. I., 1994, PANAMERICAN MATH J, V4, P39
[2]  
Alber Y.I., 1996, LECT NOTES PURE APPL, P15
[3]  
[Anonymous], 1990, MATH ITS APPL
[4]  
Aoyama K., 2009, P 5 INT C NONL AN CO, V10, P7
[5]  
Aoyama K, 2007, FIXED POINT THEOR-RO, V8, P143
[6]   Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space [J].
Aoyama, Koji ;
Kimura, Yasunori ;
Takahashi, Wataru ;
Toyoda, Masashi .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (08) :2350-2360
[7]   Strongly relatively nonexpansive sequences in Banach spaces and applications [J].
Aoyama, Koji ;
Kohsaka, Fumiaki ;
Takahashi, Wataru .
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2009, 5 (02) :201-225
[8]  
Barbu V, 1976, Nonlinear Semigroups and Differential Equations in Banach Spaces, Editura Academiei Republicii Socialiste Romania
[9]   Bregman monotone optimization algorithms [J].
Bauschke, HH ;
Borwein, JM ;
Combettes, PL .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2003, 42 (02) :596-636
[10]   NONLINEAR MAXIMAL MONOTONE OPERATORS IN BANACH SPACE [J].
BROWDER, FE .
MATHEMATISCHE ANNALEN, 1968, 175 (02) :89-&
12345