Generalized Convexity, Generalized Monotonicity: Recent Results

Jean-Pierre Crouzeix

ISBN 10: 1461333431 / ISBN 13: 9781461333432

Published by Springer US, Springer US Okt 2011, 2011

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 492 pp. Englisch.

Seller Inventory # 9781461333432

Bibliographic Details

• Title: Generalized Convexity, Generalized Monotonicity: Recent Results
• Publisher: Springer US, Springer US Okt 2011
• Publication Date: 2011
• Language: English
• ISBN 10: 1461333431
• ISBN 13: 9781461333432
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 240W x 160H x 27D millimeters 240 millimeters width by 160 millimeters height by 27 millimeters depth
• Weight: 779 grams

About this title

Synopsis

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.