Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, September 1999
Springer (2001), Lecture Notes in Economics and Mathematical Systems, Vol. 502, ISBN: 3-540-41806-7
Various generalizations of convex functions have been introduced in areas such as mathematical programming, economics, management science, engineering, stochastics and applied sciences, for example. Such functions preserve one or more properties of convex functions and give rise to models which are more adaptable to real-world situations than convex models. Similarly, generalizations of monotone maps have been studied recently. A growing literature of this interdisciplinary field has appeared, and a large number of international meetings are entirely devoted or include clusters on generalized convexity and generalized monotonicity. The present book contains a selection of refereed papers presented at the 6th International Symposium on Generalized Convexity/Monotonicity, and aims to review the latest developments in the field.
| Preface | |
| INVITED PAPERS | |
| 1. Minimization of the Sum of Several Linear Fractional Functions, Hirochi Konno | 3 |
| 2. Discrete Higher Order Convex Functions and their Applications, Andras Pekopa | 21 |
| 3. Cuts and Semidefinite Relaxations for Nonconvex Quadratic Problems, Y. Yajima, V. Ramana and P. Pardalos | 48 |
| CONTRIBUTED PAPERS | |
| 4. The Steiner Ratio of L^3_p, Jens Albrecht and Dietmar Cieslik | 73 |
| 5. Normal Cones to Sublevel Sets: An Axiomatic Approach. Applications to Quasiconvexity and Pseudoconvexity, Didier Aussel and Aris Daniilidis | 88 |
| 6. Multiobjective Programming with rho-Convex Functions, A. Beato-Moreno, R. Osuna-Gomez, A. Rufian-Lizana and P. Ruiz-Canales | 102 |
| 7. Vector Invex N-Set Functions and Minimax Programming, Davinder Bhatia and Promila Kumar | 117 |
| 8. On the Supremum in Quadratic Fractional Programming, Alberto Cambin, Laura Carosi and Laura Martein | 129 |
| 9. First and Second Order Characterizations of a Class of Pseudoconcave Vector Functions, Riccardo Cambini, Laura Marten | 144 |
| 10. New Invexity-Type Conditions in Constraint Optimization, Giuseppe Caristi, Massimiliano Ferrara and Anton Stefanescu | 159 |
| 11. Stochastic (s)-Increasing Convexity, Michel Denuit and Claude Lefevre | 167 |
| 12. Fixed Point Theorems, Coincidence Theorems and Variational Inequalities, B. Djafari-Rouhani, E. Tarafdar and P.J. Watson | 183 |
| 13. Representation of a Polynomial Function as a Difference of Convex Polynomials, with an Application, Albert Ferrer Biosca | 189 |
| 14. Proper Efficiency and Generalized Convexity in Nonsmooth Vector Optimization Problems, Giorgio Giorgi and Angelo Guerraggio | 208 |
| 15. Duality for Fractional Min-Max Problems Involving Arcwise Connected and Generalized Arcwise Connected Functions, Pankaj Gupta and Davinder Bhatia | 218 |
| 16. Generalized Convexity for Unbounded Sets: The Enlarged Space, Guillermo L. Hansen and Jean-Claude Dupin | 231 |
| 17. A Note on Minty Variational Inequalities and Generalized Monotonicity, Reinhard John | 240 |
| 18. On Vector Equilibrium and Vector Variational Inequality Problems, Igor V. Konnov | 247 |
| 19. Stochastic Orders Generated by Generalized Convex Functions, Alfred Mueller | 264 |
| 20. Separation Theorems for Convex Sets and Convex Functions with Invariance Properties, Zsolt Pales | 279 |
| 21. Convexity and Generalized Convexity Methods for the Study of Hamilton-Jacobi Equations, Jean-Paul Penot and Michel Volle | 294 |
| 22. Higher-Order Monotone Functions and Probability Theory, Dinis D. Pestana and Sandra Mendonca | 317 |
| 23. Convexity and Decomposability in Multivalued Analysis, Andrian Petrusel and Ghiosel Mot | 332 |
| 24. Scalar Characterizations of Generalized Convex Functions, Nicolae Popovici | 341 |
| 25. Optimality and Wolfe Duality for Multiobjective Programming Problems Involving N-Set Functions, Vasile Preda and Ion M. Stancu-Minasian | 349 |
| 26. Vector Stochastic Optimization Problems, Giovanna Redaelli | 362 |
| 27. On Suprema of Abstract Convex and Quasi-Convex Hulls, Ivan Singer | 381 |
| 28. Specific Numerical Methods for Solving Some Special Max-Min Programming Problems Involving Generalized Convex Functions, Stefan Tigan, Ion M. Stancu-Minasian and Iliana Tigan | 395 |