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

Phelps, Robert R.

 
9783540567158: Convex Functions, Monotone Operators and Differentiability (Lecture Notes in Mathematics): 1364
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ISBN 10: 3540567151 ISBN 13: 9783540567158
Editorial: Springer, 1993

Sinopsis

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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Reseña del editor

In the three and a half years since the first edition to these notes was written there has been progress on a number of relevant topics. D. Preiss answered in the affirmative the decades old question of whether a Banach space with an equivalent Gateaux differentiable norm is a weak Asplund space, while R. Haydon constructed some very ingenious examples which show, among other things, that the converse to Preiss' theorem is false. S. Simons produced a startlingly simple proof of Rockafellar's maximal monotonicity theorem for subdifferentials of convex functions. G. Godefroy, R. Deville and V. Zizler proved an exciting new version ofthe Borwein-Preiss smooth variational prin­ ciple. Other new contributions to the area have come from J. Borwein, S. Fitzpatrick, P. Kenderov, 1. Namioka, N. Ribarska, A. and M. E. Verona and the author. Some ofthe new material and substantial portions ofthe first edition were used in a one-quarter graduate course at the University of Washington in 1991 (leading to a number of corrections and improvements) and some of the new theorems were presented in the Rainwater Seminar. An obvious improvement is due to the fact that I learned to use '!EX. The task of converting the original MacWrite text to '!EXwas performed by Ms. Mary Sheetz, to whom I am extremely grateful.

Reseña del editor

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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Editorial
Springer
Año de publicación
1993
Idioma
Inglés
ISBN 10 
3540567151
ISBN 13 
9783540567158
Encuadernación
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Número de edición
2
Número de páginas
132
Contacto del fabricante
no disponible
Persona responsable
CMN Printpool Inh. Mathis Neumann
https://www.also.com/ec/cms5/en_6000/6000/index.jsp

Friedrich-Karl-Str. 9
Hamburg
Alemania

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9783662177792: Convex Functions, Monotone Operators and Differentiability

Edición Destacada

ISBN 10:  366217779X ISBN 13:  9783662177792
Editorial: Springer, 2014
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