The Resource Convex functions, monotone operators, and differentiability, Robert R. Phelps
Convex functions, monotone operators, and differentiability, Robert R. Phelps
Resource Information
The item Convex functions, monotone operators, and differentiability, Robert R. Phelps represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Convex functions, monotone operators, and differentiability, Robert R. Phelps represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 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 BorweinPreiss 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 RadonNikodym 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
 Language
 eng
 Edition
 2nd ed.
 Extent
 1 online resource (ix, 116 pages)
 Contents

 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
 Isbn
 9783540460770
 Label
 Convex functions, monotone operators, and differentiability
 Title
 Convex functions, monotone operators, and differentiability
 Statement of responsibility
 Robert R. Phelps
 Subject

 Convex functions
 Convex functions
 Differentiable functions
 Differentiable functions
 Differentiable functions
 Differenzierbarkeit
 Fonctions convexes
 Fonctions différentiables
 Konvexe Funktion
 Monotone operators
 Monotone operators
 Monotone operators
 Monotoner Operator
 Opérateurs monotones
 Convex functions
 Language
 eng
 Summary
 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 BorweinPreiss 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 RadonNikodym 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
 Action
 digitized
 Cataloging source
 SPLNM
 http://library.link/vocab/creatorDate
 19262013
 http://library.link/vocab/creatorName
 Phelps, Robert R.
 Dewey number
 515.7
 Illustrations
 illustrations
 Index
 index present
 LC call number

 QA3
 QA331.5
 LC item number
 .L28 no. 1364 1993
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Lecture notes in mathematics,
 Series volume
 1364
 http://library.link/vocab/subjectName

 Convex functions
 Monotone operators
 Differentiable functions
 Fonctions convexes
 Opérateurs monotones
 Fonctions différentiables
 Convex functions
 Differentiable functions
 Monotone operators
 Konvexe Funktion
 Differenzierbarkeit
 Monotoner Operator
 Label
 Convex functions, monotone operators, and differentiability, Robert R. Phelps
 Bibliography note
 Includes bibliographical references (pages 110114) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 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
 Control code
 288913453
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (ix, 116 pages)
 Form of item
 online
 Isbn
 9783540460770
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations.
 Reproduction note
 Electronic reproduction.
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)288913453
 System details
 Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
 Label
 Convex functions, monotone operators, and differentiability, Robert R. Phelps
 Bibliography note
 Includes bibliographical references (pages 110114) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 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
 Control code
 288913453
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (ix, 116 pages)
 Form of item
 online
 Isbn
 9783540460770
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations.
 Reproduction note
 Electronic reproduction.
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)288913453
 System details
 Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Subject
 Convex functions
 Convex functions
 Differentiable functions
 Differentiable functions
 Differentiable functions
 Differenzierbarkeit
 Fonctions convexes
 Fonctions différentiables
 Konvexe Funktion
 Monotone operators
 Monotone operators
 Monotone operators
 Monotoner Operator
 Opérateurs monotones
 Convex functions
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