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The Resource An easy path to convex analysis and applications, Boris S. Mordukhovich, Nguyen Mau Nam

An easy path to convex analysis and applications, Boris S. Mordukhovich, Nguyen Mau Nam

Label
An easy path to convex analysis and applications
Title
An easy path to convex analysis and applications
Statement of responsibility
Boris S. Mordukhovich, Nguyen Mau Nam
Creator
Contributor
Author
Subject
Language
eng
Summary
Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build the theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the Fermat-Torricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications
Member of
Cataloging source
CaBNVSL
Citation source
  • Compendex
  • INSPEC
  • Google scholar
  • Google book search
http://library.link/vocab/creatorName
Mordukhovich, B. Sh.
Dewey number
516.08
Illustrations
illustrations
Index
index present
LC call number
QA331.5
LC item number
.M668 2014
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Nguyen, Mau Nam
Series statement
Synthesis lectures on mathematics and statistics,
Series volume
#14
http://library.link/vocab/subjectName
  • Mathematical analysis
  • Convex functions
  • Convex geometry
  • Nonsmooth optimization
  • MATHEMATICS
  • Convex functions
  • Convex geometry
  • Mathematical analysis
  • Nonsmooth optimization
Target audience
  • adult
  • specialized
Label
An easy path to convex analysis and applications, Boris S. Mordukhovich, Nguyen Mau Nam
Instantiates
Publication
Copyright
Bibliography note
Includes bibliographical references (pages 195-197) 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
  • Convex sets and functions -- Subdifferential calculus -- Remarkable consequences of convexity -- Applications to optimization and location problems
  • 1. Convex sets and functions -- 1.1 Preliminaries -- 1.2 Convex sets -- 1.3 Convex functions -- 1.4 Relative interiors of convex sets -- 1.5 The distance function -- 1.6 Exercises for chapter 1
  • 2. Subdifferential calculus -- 2.1 Convex separation -- 2.2 Normals to convex sets -- 2.3 Lipschitz continuity of convex functions -- 2.4 Subgradients of convex functions -- 2.5 Basic calculus rules -- 2.6 Subgradients of optimal value functions -- 2.7 Subgradients of support functions -- 2.8 Fenchel conjugates -- 2.9 Directional derivatives -- 2.10 Subgradients of supremum functions -- 2.11 Exercises for chapter 2
  • 3. Remarkable consequences of convexity -- 3.1 Characterizations of differentiability -- 3.2 Carathéodory theorem and Farkas Lemma -- 3.3 Radon theorem and Helly theorem -- 3.4 Tangents to convex sets -- 3.5 Mean value theorems -- 3.6 Horizon cones -- 3.7 Minimal time functions and Minkowski gauge -- 3.8 Subgradients of minimal time functions -- 3.9 Nash equilibrium -- 3.10 Exercises for chapter 3
  • 4. Applications to optimization and location problems -- 4.1 Lower semicontinuity and existence of minimizers -- 4.2 Optimality conditions -- 4.3 Subgradient methods in convex optimization -- 4.4 The Fermat-Torricelli problem -- 4.5 A generalized Fermat-Torricelli problem -- 4.6 A generalized Sylvester problem -- 4.7 Exercises for chapter 4
  • Solutions and hints for exercises -- Bibliography -- Authors' biographies -- Index
Control code
868155830
Dimensions
unknown
Extent
1 online resource (xvi, 202 pages)
File format
multiple file formats
Form of item
online
Isbn
9781627052382
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.2200/S00554ED1V01Y201312MAS014
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
cl0500000416
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)868155830
Label
An easy path to convex analysis and applications, Boris S. Mordukhovich, Nguyen Mau Nam
Publication
Copyright
Bibliography note
Includes bibliographical references (pages 195-197) 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
  • Convex sets and functions -- Subdifferential calculus -- Remarkable consequences of convexity -- Applications to optimization and location problems
  • 1. Convex sets and functions -- 1.1 Preliminaries -- 1.2 Convex sets -- 1.3 Convex functions -- 1.4 Relative interiors of convex sets -- 1.5 The distance function -- 1.6 Exercises for chapter 1
  • 2. Subdifferential calculus -- 2.1 Convex separation -- 2.2 Normals to convex sets -- 2.3 Lipschitz continuity of convex functions -- 2.4 Subgradients of convex functions -- 2.5 Basic calculus rules -- 2.6 Subgradients of optimal value functions -- 2.7 Subgradients of support functions -- 2.8 Fenchel conjugates -- 2.9 Directional derivatives -- 2.10 Subgradients of supremum functions -- 2.11 Exercises for chapter 2
  • 3. Remarkable consequences of convexity -- 3.1 Characterizations of differentiability -- 3.2 Carathéodory theorem and Farkas Lemma -- 3.3 Radon theorem and Helly theorem -- 3.4 Tangents to convex sets -- 3.5 Mean value theorems -- 3.6 Horizon cones -- 3.7 Minimal time functions and Minkowski gauge -- 3.8 Subgradients of minimal time functions -- 3.9 Nash equilibrium -- 3.10 Exercises for chapter 3
  • 4. Applications to optimization and location problems -- 4.1 Lower semicontinuity and existence of minimizers -- 4.2 Optimality conditions -- 4.3 Subgradient methods in convex optimization -- 4.4 The Fermat-Torricelli problem -- 4.5 A generalized Fermat-Torricelli problem -- 4.6 A generalized Sylvester problem -- 4.7 Exercises for chapter 4
  • Solutions and hints for exercises -- Bibliography -- Authors' biographies -- Index
Control code
868155830
Dimensions
unknown
Extent
1 online resource (xvi, 202 pages)
File format
multiple file formats
Form of item
online
Isbn
9781627052382
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.2200/S00554ED1V01Y201312MAS014
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
cl0500000416
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)868155830

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