Generalized Convexity, Generalized Monotonicity and Applications

This volume contains a collection of refereed articles on generalized convexity and generalized monotonicity. The first part of the book contains invited papers by leading experts (J.M. Borwein, R.E. Burkard, B.S. Mordukhovich and H. Tuy) with applications of (generalized) convexity to such diverse fields as algebraic dynamics of the Gamma function values, discrete optimization, Lipschitzian stability of parametric constraint systems, and monotonicity of functions. The second part contains contributions presenting the latest developments in generalized convexity and generalized monotonicity: its connections with discrete and with continuous optimization, multiobjective optimization, fractional programming, nonsmooth Aanalysis, variational inequalities, and its applications to concrete problems such as finding equilibrium prices in mathematical economics, or hydrothermal scheduling.

Audience

This volume is suitable for faculty, graduate students, and researchers in mathematical programming, operations research, convex analysis, nonsmooth analysis, game theory and mathematical economics.

Zusammenfassung
In recent years there is a growing interest in generalized convex fu- tions and generalized monotone mappings among the researchers of - plied mathematics and other sciences. This is due to the fact that mathematical models with these functions are more suitable to describe problems of the real world than models using conventional convex and monotone functions. Generalized convexity and monotonicity are now considered as an independent branch of applied mathematics with a wide range of applications in mechanics, economics, engineering, finance and many others. The present volume contains 20 full length papers which reflect c- rent theoretical studies of generalized convexity and monotonicity, and numerous applications in optimization, variational inequalities, equil- rium problems etc. All these papers were refereed and carefully selected from invited talks and contributed talks that were presented at the 7th International Symposium on Generalized Convexity/Monotonicity held in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is or- nized by the Working Group on Generalized Convexity (WGGC) every 3 years and aims to promote and disseminate research on the field. The WGGC (http://www.genconv.org) consists of more than 300 researchers coming from 36 countries.

Inhalt
Invited Papers.- Algebraic Dynamics of Certain Gamma Function Values.- (Generalized) Convexity and Discrete Optimization.- Lipschitzian Stability of Parametric Constraint Systems in Infinite Dimensions.- Monotonicity in the Framework of Generalized Convexity.- Contributed Papers.- On the Contraction and Nonexpansiveness Properties of the Marginal Mappings in Generalized Variational Inequalities Involving Co-Coercive Operators.- A Projection-Type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities.- Duality in Multiobjective Optimization Problems with Set Constraints.- Duality in Fractional Programming Problems with Set Constraints.- On the Pseudoconvexity of the Sum of Two Linear Fractional Functions.- Bonnesen-Type Inequalities and Applications.- Characterizing Invex and Related Properties.- Minty Variational Inequality and Optimization: Scalar and Vector Case.- Second Order Optimality Conditions for Nonsmooth Multiobjective Optimization Problems.- Second Order Subdifferentials Constructed Using Integral Convolutions Smoothing.- Applying Global Optimization to a Problem in Short-Term Hydrothermal Scheduling.- ?-Optimality for Nonsmooth Programming on a Hilbert Space.- Identification of Hidden Convex Minimization Problems.- On Vector Quasi-Saddle Points of Set-Valued Maps.- New Generalized Invexity for Duality in Multiobjective Programming Problems Involving N-Set Functions.- Equilibrium Prices and Quasiconvex Duality.