Handbook of Generalized Convexity and Generalized Monotonicity

 

Nicolas Hadjisavvas,  Sandor Komlosi,  Siegfried Schaible  (editors)

Springer (2005), Nonconvex Optimization and Its Applications, Vol.  76,  ISBN: 0-387-23255-9


Description

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.


Contents

Preface  vii
Contributing Authors xvii
   
 Part I         GENERALIZED CONVEXITY  
   

1. Introduction to Convex and Quasiconvex Analysis, Johannes B.G. Frenk, Gabor Kassay

3

2. Criteria for Generalized Convexity and Generalized Monotonicity in the Differentiable Case,  Jean-Pierre Crouzeix

89
3. Continuity and Differentiability of Quasiconvex Functions,  Jean-Pierre Crouzeix 121
4. Generalized Convexity and Optimality Conditions in Scalar and Vector Optimization,  Alberto Cambini and Laura Martein 151
5. Generalized Convexity in Vector Optimization , Dinh The Luc 195
6. Generalized Convex Duality and Its Economic Applications,  Juan Enrique Martinez-Legaz 237
7.  Abstract Convexity, Alexander Rubinov, Joydeep Dutta 293
8. Fractional Programming,  Johannes B.G. Frenk, Siegfried Schaible 335
   
Part II GENERALIZED MONOTONICITY  
   
9. Generalized Monotone Maps,  Nicolas Hadjisavvas, Siegfried Schaible 389
10. Generalized Convexity and Generalized Derivatives,  Sandor Komlosi 421
11. Generalized Convexity, Generalized Monotonicity and Nonsmooth Analysis,  Nicolas Hadjisavvas 465
12. Pseudomonotone Complementarity Problems and Variational  Inequalities,  Jen-Chih Yao, Ouayl Chadli 501
13. Generalized Monotone Equilibrium Problems and Variational Inequalities,  Igor Konnov 559
14. Uses of Generalized Convexity and Generalized Monotonicity in Economics,  Reinhard John 619
   
Index 667

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