ON THE CYCLIC PSEUDOMONOTONICITY AND THE PROXIMAL POINT ALGORITHM

被引：2

作者：

Khatibzadeh, Hadi ^{[1
]}

Mohebbi, Vahid ^{[1
]}

Alizadeh, Mohammad Hossein ^{[2
]}

机构：

[1] Univ Zanjan, Dept Math, POB 45195-313, Zanjan, Iran

[2] Inst Adv Studies Basic Sci, Dept Math, POB 45195-1159, Zanjan, Iran

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2018年 / 8卷 / 04期

关键词：

Equilibrium problem; n-pseudomonotone bifunction; cyclic pseudomonotone bifunction; proximal point algorithm; weak convergence; strong convergence;

D O I：

10.3934/naco.2018027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce various versions of cyclic pseudomonotonicity and study the relations between them. Some examples about the relation between them and monotonicity are also presented. By imposing some assumptions on the cyclic pseudomonotone bifunctions, we study the convergence analysis of the proximal point algorithm which has been studied by Iusem and Sosa [5] for pseudomonotone bifunctions, with better assumptions.

引用

页码：441 / 449

页数：9

共 11 条

[1] EXISTENCE AND ASYMPTOTIC BEHAVIOUR FOR SOLUTIONS OF DYNAMICAL EQUILIBRIUM SYSTEMS [J].

Chbani, Zaki ;

Riahi, Hassan .

EVOLUTION EQUATIONS AND CONTROL THEORY, 2014, 3 (01) :1-14

[2] Pseudomonotone Operators: A Survey of the Theory and Its Applications [J].

Hadjisavvas, N. ;

Schaible, S. ;

Wong, N. -C. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2012, 152 (01) :1-20

[3] Maximal monotonicity of bifunctions [J].

Hadjisavvas, N. ;

Khatibzadeh, H. .

OPTIMIZATION, 2010, 59 (02) :147-160

[4] On certain conditions for the existence of solutions of equilibrium problems [J].

Iusem, Alfredo N. ;

Kassay, Gabor ;

Sosa, Wilfredo .

MATHEMATICAL PROGRAMMING, 2009, 116 (1-2) :259-273

[5] On the proximal point method for equilibrium problems in Hilbert spaces [J].

Iusem, Alfredo N. ;

Sosa, Wilfredo .

OPTIMIZATION, 2010, 59 (08) :1259-1274

[6] Proximal point algorithm for infinite pseudo-monotone bifunctions [J].

Khatibzadeh, Hadi ;

Mohebbi, Vahid .

OPTIMIZATION, 2016, 65 (08) :1629-1639

[7] Convergence analysis of the proximal point algorithm for pseudo-monotone equilibrium problems [J].

Khatibzadeh, Hadi ;

Mohebbi, Vahid ;

Ranjbar, Sajad .

OPTIMIZATION METHODS & SOFTWARE, 2015, 30 (06) :1146-1163

[8]

MARTINET B, 1970, REV FR INFORM RECH O, V4, P154

[9] On Nash-Cournot oligopolistic market equilibrium models with concave cost functions [J].

Muu, Le D. ;

Nguyen, V. H. ;

Quy, N. V. .

JOURNAL OF GLOBAL OPTIMIZATION, 2008, 41 (03) :351-364

[10] Dual extragradient algorithms extended to equilibrium problems [J].

Quoc, Tran D. ;

Anh, Pham N. ;

Muu, Le D. .

JOURNAL OF GLOBAL OPTIMIZATION, 2012, 52 (01) :139-159

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