skip to content
Convex analysis and optimization Preview this item
ClosePreview this item
Checking...

Convex analysis and optimization

Author: Dimitri P Bertsekas; Angelia Nedić; Asuman E Ozdaglar
Publisher: Belmont, Mass. : Athena Scientific, ©2003.
Series: Athena Scientific optimization and computation series.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
This book focuses on the theory of convex sets and functions, and its connections with a number of topics that span a broad range from continuous to discrete optimization. These topics include Lagrange multiplier theory, Lagrangian and conjugate/Fenchel duality, minimax theory, and nondifferentiable optimization. The book evolved from a set of lecture notes for a graduate course at M.I.T. It is widely recognized  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Document Type: Book
All Authors / Contributors: Dimitri P Bertsekas; Angelia Nedić; Asuman E Ozdaglar
ISBN: 1886529450 9781886529458
OCLC Number: 52164213
Description: xv, 534 pages : illustrations ; 24 cm.
Contents: 1. Basic convexity concepts --
2. Convexity and optimization --
3. Polyhedral convexity --
4. Subgradients and constrained optimization --
5. Lagrange multipliers --
6. Lagrangian duality --
7. Conjugate duality --
8. Dual computational methods.
Series Title: Athena Scientific optimization and computation series.
Responsibility: Dimitri P. Bertsekas with Angelia Nedić and Asuman E. Ozdaglar.

Abstract:

This book focuses on the theory of convex sets and functions, and its connections with a number of topics that span a broad range from continuous to discrete optimization. These topics include Lagrange multiplier theory, Lagrangian and conjugate/Fenchel duality, minimax theory, and nondifferentiable optimization. The book evolved from a set of lecture notes for a graduate course at M.I.T. It is widely recognized that, aside from being an eminently useful subject in engineering, operations research, and economics, convexity is an excellent vehicle for assimilating some of the basic concepts of real analysis within an intuitive geometrical setting. Unfortunately, the subject's coverage in academic curricula is scant and incidental. We believe that at least part of the reason is the shortage of textbooks that are suitable for classroom instruction, particularly for nonmathematics majors. We have therefore tried to make convex analysis accessible to a broader audience by emphasizing its geometrical character, while maintaining mathematical rigor. We have included as many insightful illustrations as possible, and we have used geometric visualization as a principal tool for maintaining the students' interest in mathematical proofs. Our treatment of convexity theory is quite comprehensive, with all major aspects of the subject receiving substantial treatment. The mathematical prerequisites are a course in linear algebra and a course in real analysis in finite dimensional spaces (which is the exclusive setting of the book). A summary of this material, without proofs, is provided in Section 1.1. The coverage of the theory has been significantly extended in the exercises, which represent a major component of the book. Detailed solutions of all the exercises (nearly 200 pages) are internet-posted in the book's www page. --

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/52164213> # Convex analysis and optimization
    a schema:CreativeWork, schema:Book ;
   library:oclcnum "52164213" ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/9410734#Place/belmont_mass> ; # Belmont, Mass.
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/mau> ;
   schema:about <http://id.worldcat.org/fast/877260> ; # Convex functions
   schema:about <http://dewey.info/class/519.76/e21/> ;
   schema:about <http://experiment.worldcat.org/entity/work/data/9410734#Topic/analyse_wiskunde> ; # Analyse (wiskunde)
   schema:about <http://id.worldcat.org/fast/1038808> ; # Nonlinear programming
   schema:about <http://experiment.worldcat.org/entity/work/data/9410734#Topic/tillampad_matematik> ; # Tillämpad matematik
   schema:about <http://experiment.worldcat.org/entity/work/data/9410734#Topic/convexe_functies> ; # Convexe functies
   schema:about <http://experiment.worldcat.org/entity/work/data/9410734#Topic/programacao_matematica> ; # Programação matemática
   schema:about <http://experiment.worldcat.org/entity/work/data/9410734#Topic/programacao_convexa> ; # Programação convexa
   schema:about <http://experiment.worldcat.org/entity/work/data/9410734#Topic/optimaliseren> ; # Optimaliseren
   schema:about <http://experiment.worldcat.org/entity/work/data/9410734#Topic/convexe_verzamelingen> ; # Convexe verzamelingen
   schema:about <http://id.worldcat.org/fast/1012099> ; # Mathematical optimization
   schema:bookFormat bgn:PrintBook ;
   schema:contributor <http://viaf.org/viaf/6041771> ; # Asuman E. Ozdaglar
   schema:contributor <http://viaf.org/viaf/16911134> ; # Angelia Nedić
   schema:copyrightYear "2003" ;
   schema:creator <http://experiment.worldcat.org/entity/work/data/9410734#Person/bertsekas_dimitri_p> ; # Dimitri P. Bertsekas
   schema:datePublished "2003" ;
   schema:description "1. Basic convexity concepts -- 2. Convexity and optimization -- 3. Polyhedral convexity -- 4. Subgradients and constrained optimization -- 5. Lagrange multipliers -- 6. Lagrangian duality -- 7. Conjugate duality -- 8. Dual computational methods."@en ;
   schema:description "This book focuses on the theory of convex sets and functions, and its connections with a number of topics that span a broad range from continuous to discrete optimization. These topics include Lagrange multiplier theory, Lagrangian and conjugate/Fenchel duality, minimax theory, and nondifferentiable optimization. The book evolved from a set of lecture notes for a graduate course at M.I.T. It is widely recognized that, aside from being an eminently useful subject in engineering, operations research, and economics, convexity is an excellent vehicle for assimilating some of the basic concepts of real analysis within an intuitive geometrical setting. Unfortunately, the subject's coverage in academic curricula is scant and incidental. We believe that at least part of the reason is the shortage of textbooks that are suitable for classroom instruction, particularly for nonmathematics majors. We have therefore tried to make convex analysis accessible to a broader audience by emphasizing its geometrical character, while maintaining mathematical rigor. We have included as many insightful illustrations as possible, and we have used geometric visualization as a principal tool for maintaining the students' interest in mathematical proofs. Our treatment of convexity theory is quite comprehensive, with all major aspects of the subject receiving substantial treatment. The mathematical prerequisites are a course in linear algebra and a course in real analysis in finite dimensional spaces (which is the exclusive setting of the book). A summary of this material, without proofs, is provided in Section 1.1. The coverage of the theory has been significantly extended in the exercises, which represent a major component of the book. Detailed solutions of all the exercises (nearly 200 pages) are internet-posted in the book's www page. --"@en ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/9410734> ;
   schema:inLanguage "en" ;
   schema:isPartOf <http://experiment.worldcat.org/entity/work/data/9410734#Series/athena_scientific_optimization_and_computation_series> ; # Athena Scientific optimization and computation series.
   schema:name "Convex analysis and optimization"@en ;
   schema:productID "52164213" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/52164213#PublicationEvent/belmont_mass_athena_scientific_2003> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/9410734#Agent/athena_scientific> ; # Athena Scientific
   schema:workExample <http://worldcat.org/isbn/9781886529458> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/52164213> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/9410734#Agent/athena_scientific> # Athena Scientific
    a bgn:Agent ;
   schema:name "Athena Scientific" ;
    .

<http://experiment.worldcat.org/entity/work/data/9410734#Person/bertsekas_dimitri_p> # Dimitri P. Bertsekas
    a schema:Person ;
   schema:familyName "Bertsekas" ;
   schema:givenName "Dimitri P." ;
   schema:name "Dimitri P. Bertsekas" ;
    .

<http://experiment.worldcat.org/entity/work/data/9410734#Place/belmont_mass> # Belmont, Mass.
    a schema:Place ;
   schema:name "Belmont, Mass." ;
    .

<http://experiment.worldcat.org/entity/work/data/9410734#Series/athena_scientific_optimization_and_computation_series> # Athena Scientific optimization and computation series.
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/52164213> ; # Convex analysis and optimization
   schema:name "Athena Scientific optimization and computation series." ;
   schema:name "Athena Scientific optimization and computation series" ;
    .

<http://experiment.worldcat.org/entity/work/data/9410734#Topic/analyse_wiskunde> # Analyse (wiskunde)
    a schema:Intangible ;
   schema:name "Analyse (wiskunde)"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/9410734#Topic/convexe_verzamelingen> # Convexe verzamelingen
    a schema:Intangible ;
   schema:name "Convexe verzamelingen"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/9410734#Topic/programacao_convexa> # Programação convexa
    a schema:Intangible ;
   schema:name "Programação convexa"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/9410734#Topic/programacao_matematica> # Programação matemática
    a schema:Intangible ;
   schema:name "Programação matemática"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/9410734#Topic/tillampad_matematik> # Tillämpad matematik
    a schema:Intangible ;
   schema:name "Tillämpad matematik"@en ;
    .

<http://id.worldcat.org/fast/1012099> # Mathematical optimization
    a schema:Intangible ;
   schema:name "Mathematical optimization"@en ;
    .

<http://id.worldcat.org/fast/1038808> # Nonlinear programming
    a schema:Intangible ;
   schema:name "Nonlinear programming"@en ;
    .

<http://id.worldcat.org/fast/877260> # Convex functions
    a schema:Intangible ;
   schema:name "Convex functions"@en ;
    .

<http://viaf.org/viaf/16911134> # Angelia Nedić
    a schema:Person ;
   schema:familyName "Nedić" ;
   schema:givenName "Angelia" ;
   schema:name "Angelia Nedić" ;
    .

<http://viaf.org/viaf/6041771> # Asuman E. Ozdaglar
    a schema:Person ;
   schema:familyName "Ozdaglar" ;
   schema:givenName "Asuman E." ;
   schema:name "Asuman E. Ozdaglar" ;
    .

<http://worldcat.org/isbn/9781886529458>
    a schema:ProductModel ;
   schema:isbn "1886529450" ;
   schema:isbn "9781886529458" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.