Journal of Convex Analysis 27 (2020), No. 3, 959--977
Copyright Heldermann Verlag 2020
Yosida Approximation Methods for Generalized Equilibrium Problems
Pham Ngoc Anh
Inst. for Research and Application of Optimization, VinTech, Vingroup, Vietnam
v.anhpn27@vinoptima.org
Hoai An Le Thi
Inst. for Research and Application of Optimization, VinTech, Vingroup, Vietnam
vinoptima01@vinoptima.org
Pham Dinh Tao
Inst. for Research and Application of Optimization, VinTech, Vingroup, Vietnam
vinoptima02@vinoptima.org
We present new iteration methods, which are called Yosida approximation methods, for finding a critical point of generalized equilibrium problems. The methods are based on the idea of the DC (Difference of convex functions) decomposition method and Yosida regularization method. We show that the iterative sequences generated by the methods converge to a critical point under mild assumptions on parameters. Application to the Cournot-Nash oligopolistic market model with concave cost functions is reported.
Keywords: Equilibrium problems, pseudomonotonicity, Yosida regularization, critical point, projection method.
MSC: 65K10, 90C25, 49J35.
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