Maximal monotonicity of bifunctions

被引：54

作者：

Hadjisavvas, N. ^{[1
]}

Khatibzadeh, H. ^{[2
]}

机构：

[1] Univ Aegean, Dept Product & Syst Design Engn, Syros, Greece

[2] Tarbiat Modares Univ, Dept Math, Tehran, Iran

来源：

OPTIMIZATION | 2010年 / 59卷 / 02期

关键词：

equilibrium problem; monotone bifunctions; maximal monotone operators; cyclic monotonicity;

D O I：

10.1080/02331930801951116

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：

For each monotone bifunction F defined on a subset C of a Banach space, an associated monotone operator AF can be defined. The bifunction F is called maximal monotone, if AF is maximal monotone. We find conditions for a bifunction to be maximal monotone and show the relation to the existence of solutions of an equilibrium problem. Also, we establish some properties of the domain C when F is maximal monotone. Finally, we define and study cyclically monotone bifunctions.

引用

页码：147 / 160

页数：14

共 11 条

[1] Ait Mansour M., 2003, COMMUN APPL ANAL, V7, P369
[2] Blum E., 1994, Math. Stud., V63, P127
[3] Maximality of sums of two maximal monotone operators
Borwein, Jonathan M.
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (10) : 2951 - 2955
[4] Combettes PL, 2005, J NONLINEAR CONVEX A, V6, P117
[5] Iterative algorithms for equilibrium problems
Iusem, AN
Sosa, W
[J]. OPTIMIZATION, 2003, 52 (03) : 301 - 316
[6] Partial proximal point method for nonmonotone equilibrium problems
Konnov, IV
[J]. OPTIMIZATION METHODS & SOFTWARE, 2006, 21 (03) : 373 - 384
[7] MOUDAFI A, 1999, LECT NOTES EC MATH S, V477
[8] Papageorgiou N.S., 1997, HDB MULTIVALUED ANAL, V1
[9] PHELPS RR, 1993, MATHFA9302209 ARXIV
[10] CHARACTERIZATION OF SUBDIFFERENTIALS OF CONVEX FUNCTIONS
ROCKAFEL.RT
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1966, 17 (03) : 497 - &

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