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A PROXIMAL POINT-TYPE ALGORITHM FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS
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 Title & Authors
A PROXIMAL POINT-TYPE ALGORITHM FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS
Kim, Jong-Kyu; Anh, Pham Ngoc; Hyun, Ho-Geun;
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 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, . 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;
 Language
English
 Cited by
1.
On ergodic algorithms for equilibrium problems, Journal of Global Optimization, 2016, 64, 1, 179  crossref(new windwow)
2.
Two new splitting algorithms for equilibrium problems, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017, 111, 4, 1051  crossref(new windwow)
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