Overview

A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo­ metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man­ agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob­ lems.

Full Product Details

Author:   Jean-Pierre Crouzeix ,  Juan Enrique Martinez Legaz ,  Michel Volle
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1998
Volume:   27
Dimensions:   Width: 16.00cm , Height: 2.50cm , Length: 24.00cm
Weight:   0.779kg
ISBN:  

9781461333432

ISBN 10:   1461333431
Pages:   471
Publication Date:   12 October 2011
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Preface. Part I: Generalized Convexity. 1. Are Generalized Derivatives Useful for Generalized Convex Functions? J.-P. Penot. 2. Stochastic 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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