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http://dx.doi.org/10.4134/BKMS.2012.49.4.749

A PROXIMAL POINT-TYPE ALGORITHM FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS  

Kim, Jong-Kyu (Department of Mathematics Education Kyungnam University)
Anh, Pham Ngoc (Department of Mathematics Education Kyungnam University)
Hyun, Ho-Geun (Department of Mathematics Education Kyungnam University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.4, 2012 , pp. 749-759 More about this Journal
Abstract
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, ${\nabla}({\parallel}x{\parallel}^2_M)$. 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.
Keywords
equilibrium problems; proximal point algorithm; pseudomonotonicity; linear proximal function; Banach contraction method;
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