Convex Functions, Monotone Operators and Differentiability (Lecture Notes in Mathematics): 1364 - Brossura

Phelps, Robert R.

Brossura

ISBN 10: 3540567151 ISBN 13: 9783540567158

Casa editrice: Springer, 1993

Riassunto

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.

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Contenuti

Convex functions on real Banach spaces.- Monotone operators, subdifferentials and Asplund spaces.- Lower semicontinuous convex functions.- Smooth variational principles, Asplund spaces, weak Asplund spaces.- Asplund spaces, the RNP and perturbed optimization.- Gâteaux differentiability spaces.- A generalization of monotone operators: Usco maps.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 3540567151
• ISBN 13: 9783540567158
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 132
• Contatto del produttore: non disponibile
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