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
Resource Information
The item An easy path to convex analysis and applications, Boris S. Mordukhovich, Nguyen Mau Nam 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 An easy path to convex analysis and applications, Boris S. Mordukhovich, Nguyen Mau Nam 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
 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 FermatTorricelli 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
 Language
 eng
 Extent
 1 online resource (xvi, 202 pages)
 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 FermatTorricelli problem  4.5 A generalized FermatTorricelli problem  4.6 A generalized Sylvester problem  4.7 Exercises for chapter 4
 Solutions and hints for exercises  Bibliography  Authors' biographies  Index
 Isbn
 9781627052382
 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
 Subject

 Convex functions
 Convex geometry
 Convex geometry
 Fenchel conjugate
 FermatTorricelli problem
 Helly theorem
 MATHEMATICS  Geometry  General
 Mathematical analysis
 Mathematical analysis
 Nash equilibrium
 Nonsmooth optimization
 Nonsmooth optimization
 Radon theorem
 Weiszfeld algorithm
 convex function
 convex set
 directional derivative
 distance function
 generalized differentiation
 minimal time function
 normal cone
 optimal value function
 optimization
 setvalued mapping
 smallest enclosing ball problem
 subdifferential
 subgradient
 subgradient algorithm
 support function
 Affine set
 Carathéodory theorem
 Convex functions
 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 FermatTorricelli 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
 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
 Bibliography note
 Includes bibliographical references (pages 195197) 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 FermatTorricelli problem  4.5 A generalized FermatTorricelli 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
 Bibliography note
 Includes bibliographical references (pages 195197) 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 FermatTorricelli problem  4.5 A generalized FermatTorricelli 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
Subject
 Convex functions
 Convex geometry
 Convex geometry
 Fenchel conjugate
 FermatTorricelli problem
 Helly theorem
 MATHEMATICS  Geometry  General
 Mathematical analysis
 Mathematical analysis
 Nash equilibrium
 Nonsmooth optimization
 Nonsmooth optimization
 Radon theorem
 Weiszfeld algorithm
 convex function
 convex set
 directional derivative
 distance function
 generalized differentiation
 minimal time function
 normal cone
 optimal value function
 optimization
 setvalued mapping
 smallest enclosing ball problem
 subdifferential
 subgradient
 subgradient algorithm
 support function
 Affine set
 Carathéodory theorem
 Convex functions
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Aneasypathtoconvexanalysisandapplications/AXYbu_TMk1Y/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Aneasypathtoconvexanalysisandapplications/AXYbu_TMk1Y/">An easy path to convex analysis and applications, Boris S. Mordukhovich, Nguyen Mau Nam</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>