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 A proximal point-type algorithm for pseudomonotone equilibrium problems Bull. Korean Math. Soc. 2012 Vol. 49, No. 4, 749-759 https://doi.org/10.4134/BKMS.2012.49.4.749Published online July 1, 2012 Jong Kyu Kim, Pham Ngoc Anh, and Ho Geun Hyun Kyungnam University, Kyungnam University, Kyungnam University 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, $\bigtriangledown (\|x\|^2_M)$. 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 MSC numbers : 65K10, 90C25 Downloads: Full-text PDF