Convex Functions, Monotone Operators and Differentiability

Phelps, Robert R.

ISBN 10: 3540567151 / ISBN 13: 9783540567158

Editore: Springer 1993-07, 1993

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Codice articolo 6666-IUK-9783540567158

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Titolo: Convex Functions, Monotone Operators and ...

Casa editrice: Springer 1993-07

Data di pubblicazione: 1993

Legatura: PF

Condizione: New

Edizione: seconda edizione

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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.

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.