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