Studies in generalized convexity and generalized monotonicity have significantly increased during the last two decades. Researchers with very diverse backgrounds such as mathematical programming, optimization theory, convex analysis, nonlinear analysis, nonsmooth analysis, linear algebra, probability theory, variational inequalities, game theory, economic theory, engineering, management science, equilibrium analysis, for example are attracted to this fast growing field of study. Such enormous research activity is partially due to the discovery of a rich, elegant and deep theory which provides a basis for interesting existing and potential applications in different disciplines. The handbook offers an advanced and broad overview of the current state of the field. It contains fourteen chapters written by the leading experts on the respective subject; eight on generalized convexity and the remaining six on generalized monotonicity.

The chapters are as follows: Introduction to Convex and Quasiconvex Analysis (J.B.G.Frenk, G. Kassay) Criteria for Generalized Convexity and Generalized Monotonicity in the Differentiable Case (J.-P. Crouzeix) Continuity and Differentiability of Quasiconvex Functions (J.-P. Crouzeix) Generalized Convexity and Optimality Conditions in Scalar and Vector Optimization (A. Cambini, L. Martein) Generalized Convexity in Vector Optimization (D. T. Luc) Generalized Convex Duality and Its Economic Applications (J.-E. Martínez-Legaz) Abstract Convexity (A.Rubinov, J.Dutta) Fractional programming (J.B.G. Frenk, S.Schaible) Generalized Monotone Maps (N.Hadjisavvas, S.Schaible) Generalized Convexity and Generalized Derivatives (S.Komlósi) Generalized Convexity, Generalized Monotonicity and Nonsmooth Analysis (N.Hadjisavvas) Pseudomonotone Complementarity Problems and Variational Inequalities (J.-C. Yao, O. Chadly) Generalized Monotone Equilibrium Problems and Variational Inequalities (I. Konnov) Uses of Generalized Convexity and Monotonicity in Economics (R. John)