Convex Functions, Monotone Operators and Differentiability (Lecture Notes in Mathematics) - Couverture souple

Phelps, Robert R.

 
9783540567158: Convex Functions, Monotone Operators and Differentiability (Lecture Notes in Mathematics)
Couverture souple
ISBN 10 : 3540567151 ISBN 13 : 9783540567158
Editeur : Springer, 1993

Synopsis

The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition. Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space. The startlingly simple proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for subdifferentials of convex functions. The exciting new version of the useful Borwein-Preiss smooth variational principle due to Godefroy, Deville and Zizler. The material is accessible to students who have had a course in Functional Analysis; indeed, the first edition has been used in numerous graduate seminars. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational principles and perturbed optimization. While much of this is classical, streamlined proofs found more recently are given in many instances. There are numerous exercises, many of which form an integral part of the exposition.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition. Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space. The startlingly simple proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for subdifferentials of convex functions. The exciting new version of the useful Borwein-Preiss smooth variational principle due to Godefroy, Deville and Zizler. The material is accessible to students who have had a course in Functional Analysis; indeed, the first edition has been used in numerous graduate seminars. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational principles and perturbed optimization. While much of this is classical, streamlined proofs found more recently are given in many instances. There are numerous exercises, many of which form an integral part of the exposition.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer
Date d'édition
1993
Langue
anglais
ISBN 10 
3540567151
ISBN 13 
9783540567158
Reliure
Broché
Numéro d'édition
2
Nombre de pages
132
Coordonnées du fabricant
non disponible
Personne responsable
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Autres éditions populaires du même titre

9783662177792: Convex Functions, Monotone Operators and Differentiability

Edition présentée

ISBN 10 :  366217779X ISBN 13 :  9783662177792
Editeur : Springer, 2014
Couverture souple