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Convex Functions, Monotone Operators and Differentiability : NATO Asi Series - Robert R. Phelps

Convex Functions, Monotone Operators and Differentiability

NATO Asi Series

Paperback ISBN: 9783540567158
Number Of Pages: 120

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The improved and expanded second edition containsexpositions of some major results which have been obtainedin the years since the 1st edition.Theaffirmative answer by Preiss of the decades old questionof whether a Banachspace with an equivalent Gateauxdifferentiable norm is a weak Asplund space.The startlingly simple proof by Simons of Rockafellar'sfundamental maximal monotonicity theorem forsubdifferentials of convex functions.The exciting new version of the useful Borwein-Preiss smoothvariational principle due to Godefroy, Deville and Zizler.The material is accessible to students who have had a coursein Functional Analysis; indeed, the first edition has beenused in numerous graduate seminars. Starting with convexfunctions on the line, it leads to interconnected topics inconvexity, differentiability and subdifferentiability ofconvex functions in Banach spaces, generic continuity ofmonotone operators, geometry of Banach spaces and theRadon-Nikodym property, convex analysis, variationalprinciples and perturbed optimization.While much of this is classical, streamlined proofs foundmore recently are given in many instances. There arenumerous exercises, many of which form an integral part ofthe exposition.

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.- Gateaux differentiability spaces.- A generalization of monotone operators: Usco maps.

ISBN: 9783540567158
ISBN-10: 3540567151
Series: NATO Asi Series
Audience: General
Format: Paperback
Language: English
Number Of Pages: 120
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 0.71
Weight (kg): 0.2
Edition Number: 2
Edition Type: Revised