Generalized Convexity, Generalized Monotonicity: Recent Results by Jean-Pierre Crouzeix

Generalized Convexity, Generalized Monotonicity: Recent Results by Jean-Pierre Crouzeix

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.

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ISBN 13	9780792350880
ISBN 10	079235088X
Titel	Generalized Convexity, Generalized Monotonicity: Recent Results
Autor	Jean-Pierre Crouzeix
Serie	Nonconvex Optimization And Its Applications
Buchzustand	Nicht verfügbar
Bindungsart	Hardback
Verlag	Kluwer Academic Publishers
Erscheinungsjahr	1998-08-31
Seitenanzahl	471
Hinweis auf dem Einband	Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.
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