A PROXIMAL POINT-TYPE ALGORITHM FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS

被引：10
|
作者：
Kim, Jong Kyu [1 ]
Anh, Pham Ngoc [1 ]
Hyun, Ho Geun [1 ]
机构：
[1] Kyungnam Univ, Dept Math Educ, Masan 631701, South Korea
来源：
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2012年 / 49卷 / 04期
关键词：
equilibrium problems; proximal point algorithm; pseudomonotonicity; linear proximal function; Banach contraction method; VARIATIONAL-INEQUALITIES; COMPLEMENTARITY-PROBLEMS; PRINCIPLE;
D O I：
10.4134/BKMS.2012.49.4.749
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A globally convergent algorithm for solving equilibrium problems is proposed. The algorithm is based on a proximal point algorithm (shortly (PPA)) with a positive definite matrix M which is not necessarily symmetric. The proximal function in existing (PPA) usually is the gradient of a quadratic function, namely, del(parallel to x parallel to(2)(M)). This leads to a proximal point-type algorithm. We first solve pseudomonotone equilibrium problems without Lipschitzian assumption and prove the convergence of algorithms. Next, we couple this technique with the Banach contraction method for multivalued variational inequalities. Finally some computational results are given.
引用
收藏
页码：749 / 759
页数：11
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