Bianchi, Monica; Schaible, Siegfried Equilibrium problems under generalized convexity and generalized monotonicity. (English) Zbl 1066.90080 J. Glob. Optim. 30, No. 2-3, 121-134 (2004). Summary: Generalized convex functions preserve many valuable properties of mathematical programming problems with convex functions. Generalized monotone maps allow for an extension of existence results for variational inequality problems with monotone maps. Both models are special realizations of an abstract equilibrium problem with numerous applications, especially in equilibrium analysis (e.g., Blum and Oettli, 1994). We survey existence results for equilibrium problems obtained under generalized convexity and generalized monotonicity. We consider both the scalar and the vector case. Finally existence results for a system of vector equilibrium problems under generalized convexity are surveyed which have applications to a system of vector variational inequality problems. Throughout the survey we demonstrate that the results can be obtained without the rigid assumptions of convexity and monotonicity. Cited in 38 Documents MSC: 90C25 Convex programming 91A40 Other game-theoretic models Keywords:convex optimization; equilibrium problem; generalized monotonicity PDFBibTeX XMLCite \textit{M. Bianchi} and \textit{S. Schaible}, J. Glob. Optim. 30, No. 2--3, 121--134 (2004; Zbl 1066.90080) Full Text: DOI References: [1] Allevi, E., Gnudi, A. and Konnov, I.V. (2001), Generalized vector variational inequalities over product sets, Nonlinear Analysis 47, 573-582. · Zbl 1042.49509 [2] Ansari, Q.H. and Yao, J.-C. (1999), A fixed point theorem and its applications to the system of variational inequalities, Bullettin of the Australian Mathematical Society 59, 433-442. · Zbl 0944.47037 [3] Q.H., Schaible, S. and Yao, J.-C. 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