Proceedings of the 7th International Symposium on Generalized Convexity and Generalized Monotonicity
Springer (2005), Nonconvex Optimization and Its Applications, Vol. 77, ISBN: 0-387-23638-4
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.
| Preface | ix |
| Part I INVITED PAPERS | |
| 1. Algebraic Dynamics of Certain Gamma Function Values, J.M. Borwein and K. Karamanos | 3 |
|
2. (Generalized) Convexity and Discrete Optimization, Rainer E. Burkard |
23 |
|
3. Lipschitzian Stability of Parametric Constraint Systems in Infinite Dimensions, B. Mordukhovich |
39 |
| 4. Monotonicity in the Framework of Generalized Convexity, Hoang Tuy | 61 |
| Part II CONTRIBUTED PAPERS | |
| 5. On the Contraction and Nonexpansiveness Properties of the Marginal Mappings in Generalized Variational Inequalities Involving co-Coercive Operators, Pham Ngoc Anh, Le Dung Muu, Van Hien Nguyen and Jean-Jaques Strodiot | 89 |
| 6. A Projection-Type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities, T.Q. Bao and P.Q. Khanh | 113 |
| 7. Duality in Multiobjective Optimization Problems with Set Constraints, Riccardo Cambini and Laura Carosi | 131 |
| 8. Duality in Fractional Programming Problems with Set Constraints, Riccardo Cambini, Laura Carosi and Siegfried Schaible | 147 |
| 9. On the Pseudoconvexity of the Sum of two Linear Fractional Functions, Alberto Cambini, Laura Martein and Siegfried Schaible | 161 |
| 10. Bonnesen-type Inequalities and Applications, A. Raouf Chouikha | 173 |
| 11. Characterizing Invex and Related Properties, B.D. Craven | 183 |
| 12. Minty Variational Inequality and Optimization: Scalar and Vector Case, Giovanni P. Crespi, Angelo Guerraggio and Matteo Rocca | 193 |
| 13. Second Order Optimality Conditions for Nonsmooth Multiobjective Optimization Problems, Giovanni P. Crespi, Davide La Torre and Matteo Rocca | 213 |
| 14. Second Order Subdifferentials Constructed using Integral Convolutions Smoothing, Andrew Eberhard, Michael Nyblom and Rajalingam Sivakumaram | 229 |
| 15. Applying Global Optimization to a Problem in Short-Term Hydrothermal Scheduling, Albert Ferrer | 263 |
| 16. epsilon-Optimality for Nonsmooth Programming in a Hilbert Space, Misha G. Govil and Aparna Mehra | 287 |
| 17. Identification of Hidden Convex Minimization Problems, D. Li, Z. Wu, H.W.J. Lee, Z. Yang and L. Zhang | 299 |
| 18. On Vector Quasi-Saddle Points of Set-Valued Maps, Lai-Jiu Lin and Yu-Lin Tsai | 311 |
| 19. New Generalized Invexity for Duality in Multiobjective Programming Problems Involving N-Set Functions, S.K. Mishra, S.Y. Wang, K.K. Lai and J. Shi | 321 |
| 20. Equilibrium Prices and Quasiconvex Duality, Phan Thien Thach | 341 |