Generalized Convexity and Related Topics

In mathematics generalization is one of the main activities of researchers. It opens up new theoretical horizons and broadens the ?elds of applications. Intensive study of generalized convex objects began about three decades ago when the theory of convex analysis nearly reached its perfect stage of devel- ment with the pioneering contributions of Fenchel, Moreau, Rockafellar and others. The involvement of a number of scholars in the study of generalized convex functions and generalized monotone operators in recent years is due to the quest for more general techniques that are able to describe and treat models of the real world in which convexity and monotonicity are relaxed. Ideas and methods of generalized convexity are now within reach not only in mathematics, but also in economics, engineering, mechanics, ?nance and other applied sciences. This volume of referred papers, carefully selected from the contributions delivered at the 8th International Symposium on Generalized Convexity and Monotonicity (Varese, 4-8 July, 2005), o?ers a global picture of current trends of research in generalized convexity and generalized monotonicity. It begins withthreeinvitedlecturesbyKonnov,LevinandPardalosonnumericalvar- tionalanalysis,mathematicaleconomicsandinvexity,respectively.Thencome twenty four full length papers on new achievements in both the theory of the ?eld and its applications. The diapason of the topics tackled in these cont- butions is very large. It encompasses, in particular, variational inequalities, equilibrium problems, game theory, optimization, control, numerical me- ods in solving multiobjective optimization problems, consumer preferences, discrete convexity and many others.