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The Resource Convexity and well-posed problems, Roberto Lucchetti

Convexity and well-posed problems, Roberto Lucchetti

Creator
Summary
Intended for graduate students especially in mathematics, physics, and economics, this book deals with the study of convex functions and of their behavior from the point of view of stability with respect to perturbations. The primary goal is the study of the problems of stability and well-posedness, in the convex case. Stability means the basic parameters of a minimum problem do not vary much if we slightly change the initial data. Well-posedness means that points with values close to the value of the problem must be close to actual solutions. In studying this, one is naturally led to consider perturbations of both functions and of sets. The book includes a discussion of numerous topics, including: @* hypertopologies, ie, topologies on the closed subsets of a metric space; @* duality in linear programming problems, via cooperative game theory; @* the Hahn-Banach theorem, which is a fundamental tool for the study of convex functions; @* questions related to convergence of sets of nets; @* genericity and porosity results; @* algorithms for minimizing a convex function. In order to facilitate use as a textbook, the author has included a selection of examples and exercises, varying in degree of difficulty. Robert Lucchetti is Professor of Mathematics at Politecnico di Milano. He has taught this material to graduate students at his own university, as well as the Catholic University of Brescia, and the University of Pavia
Language
eng
Work
Publication
Extent
1 online resource (xiv, 305 pages)
Contents
  • Preface
  • Convex Sets and Convex Functions: the fundamentals
  • Continuity and Gamma (X)
  • The Derivatives and the Subdifferential
  • Minima and Quasi Minima
  • The Fenchel Conjugate
  • Duality
  • Linar Programming and Game Theory.- Hypertopologies, Hyperconvergences
  • Continuity of Some Operations Between Functions
  • Well-Posed Problems
  • Generic Well-Posedness
  • More Exercises
  • Appendix A: Functional Analysis
  • Appendix B: Topology
  • Appendix C: More Game Theory
  • Appendix D: Symbols, Notations, Definitions and Important Theorems
  • References, Index
Isbn
9781441921116
Instance
Label
Convexity and well-posed problems
Title
Convexity and well-posed problems
Statement of responsibility
Roberto Lucchetti
Creator
Subject
Language
eng
Summary
Intended for graduate students especially in mathematics, physics, and economics, this book deals with the study of convex functions and of their behavior from the point of view of stability with respect to perturbations. The primary goal is the study of the problems of stability and well-posedness, in the convex case. Stability means the basic parameters of a minimum problem do not vary much if we slightly change the initial data. Well-posedness means that points with values close to the value of the problem must be close to actual solutions. In studying this, one is naturally led to consider perturbations of both functions and of sets. The book includes a discussion of numerous topics, including: @* hypertopologies, ie, topologies on the closed subsets of a metric space; @* duality in linear programming problems, via cooperative game theory; @* the Hahn-Banach theorem, which is a fundamental tool for the study of convex functions; @* questions related to convergence of sets of nets; @* genericity and porosity results; @* algorithms for minimizing a convex function. In order to facilitate use as a textbook, the author has included a selection of examples and exercises, varying in degree of difficulty. Robert Lucchetti is Professor of Mathematics at Politecnico di Milano. He has taught this material to graduate students at his own university, as well as the Catholic University of Brescia, and the University of Pavia
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1950-
http://library.link/vocab/creatorName
Lucchetti, R.
Dewey number
515/.8
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA331.5
LC item number
.L75 2006eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
CMS books in mathematics
http://library.link/vocab/subjectName
  • Canadian Mathematical Society
  • Convex functions
  • Perturbation (Mathematics)
  • Functional analysis
  • Canadian Mathematical Society
  • Perturbation (Mathematics)
  • Functional analysis
  • Convexe functies
  • Convex functions
  • Convex functions
  • Functional analysis
  • Perturbation (Mathematics)
  • Convexe functies
Label
Convexity and well-posed problems, Roberto Lucchetti
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 299-301) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Convex Sets and Convex Functions: the fundamentals -- Continuity and Gamma (X) -- The Derivatives and the Subdifferential -- Minima and Quasi Minima -- The Fenchel Conjugate -- Duality -- Linar Programming and Game Theory.- Hypertopologies, Hyperconvergences -- Continuity of Some Operations Between Functions -- Well-Posed Problems -- Generic Well-Posedness -- More Exercises -- Appendix A: Functional Analysis -- Appendix B: Topology -- Appendix C: More Game Theory -- Appendix D: Symbols, Notations, Definitions and Important Theorems -- References, Index
Control code
209913474
Dimensions
unknown
Extent
1 online resource (xiv, 305 pages)
Form of item
online
Isbn
9781441921116
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/0-387-31082-7
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-0-387-28719-5
Specific material designation
remote
System control number
(OCoLC)209913474
Label
Convexity and well-posed problems, Roberto Lucchetti
Publication
Bibliography note
Includes bibliographical references (pages 299-301) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Convex Sets and Convex Functions: the fundamentals -- Continuity and Gamma (X) -- The Derivatives and the Subdifferential -- Minima and Quasi Minima -- The Fenchel Conjugate -- Duality -- Linar Programming and Game Theory.- Hypertopologies, Hyperconvergences -- Continuity of Some Operations Between Functions -- Well-Posed Problems -- Generic Well-Posedness -- More Exercises -- Appendix A: Functional Analysis -- Appendix B: Topology -- Appendix C: More Game Theory -- Appendix D: Symbols, Notations, Definitions and Important Theorems -- References, Index
Control code
209913474
Dimensions
unknown
Extent
1 online resource (xiv, 305 pages)
Form of item
online
Isbn
9781441921116
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/0-387-31082-7
Other physical details
illustrations.
http://library.link/vocab/ext/overdrive/overdriveId
978-0-387-28719-5
Specific material designation
remote
System control number
(OCoLC)209913474

Subject

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