Extragradient methods for pseudomonotone variational inequalities

被引：46
作者：
Noor, MA [1 ]
机构：
[1] Etisalat Coll Engn, Sharjah, U Arab Emirates
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2003年 / 117卷 / 03期
关键词：
variational inequalities; projection methods; fixed points; inertial proximal methods; convergence;
D O I：
10.1023/A:1023989403613
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：
We consider and analyze some new extragradient-type methods for solving variational inequalities. The modified methods converge for a pseudomonotone operator, which is a much weaker condition than monotonicity. These new iterative methods include the projection, extragradient, and proximal methods as special cases. Our proof of convergence is very simple as compared with other methods.
引用
收藏
页码：475 / 488
页数：14
相关论文
共 25 条
[1]   On the minimizing property of a second order dissipative system in Hilbert spaces [J].
Alvarez, F .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 38 (04) :1102-1119
[2]   An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping [J].
Alvarez, F ;
Attouch, H .
SET-VALUED ANALYSIS, 2001, 9 (1-2) :3-11
[3]  
Bertsekas Dimitri P., 1989, PARALLEL DISTRIBUTED
[4]  
Gabay D., 1983, AUGMENTED LAGRANGIAN, V15, P299, DOI DOI 10.1016/S0168-2024(08)70034-1
[5]  
Giannessi F., 1995, Variational Inequalities and Network Equilibrium Problems
[6]   Two new self-adaptive projection methods for variational inequality problems [J].
Han, DR ;
Lo, HK .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2002, 43 (12) :1529-1537
[7]   Improvements of some projection methods for monotone nonlinear variational inequalities [J].
He, BS ;
Liao, LZ .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2002, 112 (01) :111-128
[8]  
He BS, 1997, APPL MATH OPT, V35, P69
[9]  
Noor M. A., 2002, J INEQUALITIES PURE, V3, P1
[10]  
Noor MA, 1999, MATH COMPUT MODEL, V29, P1, DOI 10.1016/S0895-7177(99)00058-8
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