Equilibrium Problems under Generalized Convexity and Generalized Monotonicity

Authors:
Monica Bianchi;Siegfried Schaible
Affiliations:
Istituto di Econometria e Matematica per le Applicazioni Economiche, Finanziarie ed Attuariali, Università Cattolica, Largo Gemelli 1, Milano, Italy 20123;A.G. Anderson Graduate School of Management, University of California, Riverside, USA 92521
Venue:
Journal of Global Optimization
Year:
2004

Citing 12
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Abstract

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.