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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.
List of contents
Invited Papers.- Algebraic Dynamics.- Generalized Convexity and Discrete Optimization.- Lipschitzian Stability.- Monotonicity in the Framework of Gen. Convexity.- Contributed Papers.- On the Contraction of Nenexpansiveness Properties of the Marginal Mappings.- A Projection-Type Algorithm.- Duality in Multiobjective Optimization Problems.- Duality in Fractional Programming.- On the Pseudoconvexity of the Sum.- Bonnesen-type Inequalities.- Characterizing Invex.- Minty Variational Inequality and Opt..- Second Order Optimality.- Second Order Subdifferentials.- Applying Global Opt..- E-Optimality.- Identification of Hidden Convex Minimization Problems.- On Vector Quasi-Saddle Points.- New Generalized Invexity.- Equilibrium Prices.
Summary
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.
