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 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
- 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 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
- 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
- Fermat-Torricelli 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
- set-valued 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 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
- 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 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
- 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
Subject
- Convex functions
- Convex geometry
- Convex geometry
- Fenchel conjugate
- Fermat-Torricelli 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
- set-valued 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 fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/An-easy-path-to-convex-analysis-and-applications/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/An-easy-path-to-convex-analysis-and-applications/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>
