Generalized Convexity, Generalized Monotonicity: Recent Results: Recent Results / Edition 1by Jean-Pierre Crouzeix
The geometrical structure induced by convexity in mathematical programming has many useful properties: continuity and differentiability of the functions, separability and optimality conditions, duality, sensibility of the optimal solutions, etc. Several of the most interesting ones are preserved when convexity is relaxed in quasiconvexity or pseudoconvexity (a… See more details below
The geometrical structure induced by convexity in mathematical programming has many useful properties: continuity and differentiability of the functions, separability and optimality conditions, duality, sensibility of the optimal solutions, etc. Several of the most interesting ones are preserved when convexity is relaxed in quasiconvexity or pseudoconvexity (a function is quasi-convex if its lower level sets are convex). This is still the case for variational inequalities problems when the classical monotonicity assumption on the map is relaxed in quasimonotonicity or pseudomonotonicity.
This volume contains 23 selected lectures presented at the most recent international symposium on generalized convexity. It provides an up-to-date review of recent developments.
Audience: The book will be of value to researchers and students working in economics, mathematical programming, operations research, management sciences, equilibrium problems, engineering and probability.
- Springer US
- Publication date:
- Nonconvex Optimization and Its Applications (closed) Series, #27
- Edition description:
- Product dimensions:
- 9.21(w) x 6.14(h) x 1.06(d)
Table of Contents
Preface. Part I: Generalized Convexity. 1. Are Generalized Derivatives Useful for Generalized Convex Functions? J.-P. Penot. 2. Shastic Programs with Chance Constraints: Generalized Convexity and Approximation Issues; R.J.-B. Wets. 3. Error Bounds for Convex Inequality Systems; A.S. Lewis, Jong-Shi Pang. 4. Applying Generalised Convexity Notions to Jets; A. Eberhard, et al. 5. Quasiconvexity via Two Step Functions; A.M. Rubinov, B.M. Glover. 6. On Limiting Fréchet epsilon-Subdifferentials; A. Jourani, M. Théra. 7. Convexity Space with Respect to a Given Set; L. Blaga, L. Lupsa. 8. A Convexity Condition for the Nonexistence of Some Antiproximinal Sets in the Space of Integrable Functions; A.-M. Precupanu. 9. Characterizations of rho-Convex Functions; M. Castellani, M. Pappalardo. Part II: Generalized Monotonicity. 10. Characterizations of Generalized Convexity and Generalized Monotonicity, a Survey; J.-P. Crouzeix. 11. Quasimonotonicity and Pseudomonotonicity in Variational Inequalities and Equilibrium Problems; N. Hadjisavvas, S. Schaible. 12. On the Scalarization of Pseudoconcavity and Pseudomonotonicity Concepts for Vector Valued Functions; R. Cambini, S. Komlósi. 13. Variational Inequalities and Pseudomonotone Functions: Some Characterizations; R. John. Part III: Optimality Conditions and Duality. 14. Simplified Global Optimality Conditions in Generalized Conjugation Theory; F. Flores-Bazán, J.-E. Martínez-Legaz. 15. Duality in DC Programming; B. Lemaire, M. Volle. 16. Recent Developments in Second Order Necessary Optimality Conditions; A. Cambini, et al. 17. Higher Order Invexity and Duality in Mathematical Programming; B. Mond, J. Zhang. 18. Fenchel Duality in Generalized Fractional Programming; C.R. Bector, et al. Part IV: Vector Optimization. 19. The Notion of Invexity in Vector Optimization: Smooth and Nonsmooth Case; G. Giorgi, A. Guerraggio. 20. Quasiconcavity of Sets and Connectedness of the Efficient Frontier in Ordered Vector Spaces; E. Molho, A. Zaffaroni. 21. Multiobjective Quadratic Problem: Characterization of the Efficient Points; A. Beato-Moreno, et al. 22. Generalized Concavity for Bicriteria Functions; R. Cambini. 23. Generalized Concavity in Multiobjective Programming; A. Cambini, L. Martein.
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