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Lectures on Convex Optimization
Buch von Yurii Nesterov
Sprache: Englisch

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Beschreibung
This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning.

Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail.

Researchers in theoretical optimization as well as professionals working on optimization problems will findthis book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author¿s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.
This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning.

Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail.

Researchers in theoretical optimization as well as professionals working on optimization problems will findthis book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author¿s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.
Über den Autor
¿Yurii Nesterov is a well-known specialist in optimization. He is an author of pioneering works related to fast gradient methods, polynomial-time interior-point methods, smoothing technique, regularized Newton methods, and others. He is a winner of several prestigious international prizes, including George Danzig prize (2000), von Neumann Theory prize (2009), SIAM Outstanding Paper Award (20014), and Euro Gold Medal (2016).
Zusammenfassung

Presents a self-contained description of fast gradient methods

Offers the first description in the monographic literature of the modern second-order methods based on cubic regularization

Provides a comprehensive treatment of the smoothing technique

Develops a new theory of optimization in relative scale

Inhaltsverzeichnis
Introduction.- Part I Black-Box Optimization.- 1 Nonlinear Optimization.- 2 Smooth Convex Optimization.- 3 Nonsmooth Convex Optimization.- 4 Second-Order Methods.- Part II Structural Optimization.- 5 Polynomial-time Interior-Point Methods.- 6 Primal-Dual Model of Objective Function.- 7 Optimization in Relative Scale.- Bibliographical Comments.- Appendix A. Solving some Auxiliary Optimization Problems.- References.- Index.
Details
Erscheinungsjahr: 2018
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Springer Optimization and Its Applications
Inhalt: xxiii
589 S.
1 s/w Illustr.
589 p. 1 illus.
ISBN-13: 9783319915777
ISBN-10: 3319915770
Sprache: Englisch
Herstellernummer: 978-3-319-91577-7
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Nesterov, Yurii
Auflage: 2nd ed. 2018
Hersteller: Springer International Publishing
Springer Optimization and Its Applications
Maße: 241 x 160 x 39 mm
Von/Mit: Yurii Nesterov
Erscheinungsdatum: 01.12.2018
Gewicht: 1,08 kg
Artikel-ID: 113482131
Über den Autor
¿Yurii Nesterov is a well-known specialist in optimization. He is an author of pioneering works related to fast gradient methods, polynomial-time interior-point methods, smoothing technique, regularized Newton methods, and others. He is a winner of several prestigious international prizes, including George Danzig prize (2000), von Neumann Theory prize (2009), SIAM Outstanding Paper Award (20014), and Euro Gold Medal (2016).
Zusammenfassung

Presents a self-contained description of fast gradient methods

Offers the first description in the monographic literature of the modern second-order methods based on cubic regularization

Provides a comprehensive treatment of the smoothing technique

Develops a new theory of optimization in relative scale

Inhaltsverzeichnis
Introduction.- Part I Black-Box Optimization.- 1 Nonlinear Optimization.- 2 Smooth Convex Optimization.- 3 Nonsmooth Convex Optimization.- 4 Second-Order Methods.- Part II Structural Optimization.- 5 Polynomial-time Interior-Point Methods.- 6 Primal-Dual Model of Objective Function.- 7 Optimization in Relative Scale.- Bibliographical Comments.- Appendix A. Solving some Auxiliary Optimization Problems.- References.- Index.
Details
Erscheinungsjahr: 2018
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Springer Optimization and Its Applications
Inhalt: xxiii
589 S.
1 s/w Illustr.
589 p. 1 illus.
ISBN-13: 9783319915777
ISBN-10: 3319915770
Sprache: Englisch
Herstellernummer: 978-3-319-91577-7
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Nesterov, Yurii
Auflage: 2nd ed. 2018
Hersteller: Springer International Publishing
Springer Optimization and Its Applications
Maße: 241 x 160 x 39 mm
Von/Mit: Yurii Nesterov
Erscheinungsdatum: 01.12.2018
Gewicht: 1,08 kg
Artikel-ID: 113482131
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