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Cover: 9783030947842 | Convex Analysis and Beyond | Volume I: Basic Theory | Nam (u. a.)
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Convex Analysis and Beyond
Volume I: Basic Theory
Buch von Nguyen Mau Nam (u. a.)
Sprache: Englisch

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Beschreibung
This book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications.
The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.
This book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications.
The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.
Über den Autor
Boris Mordukhovich is Distinguished University Professor of Mathematics at Wayne State University. He has more than 500 publications including several monographs. Among his best known achievements are the introduction and development of powerful constructions of generalized differentiation and their applications to broad classes of problems in variational analysis, optimization, equilibrium, control, economics, engineering, and other fields. Mordukhovich is a SIAM Fellow, an AMS Fellow, and a recipient of many international awards and honors including Doctor Honoris Causa degrees from six universities over the world. He is a Highly Cited Researcher in Mathematics. His research has been supported by continued grants from the National Science Foundations and the Air Force Office of Scientific Research.
Nguyen Mau Nam is a Professor of Mathematics at Portland State University. He has published more than 55 research articles and one book in convex analysis withapplications to optimization theory and numerical algorithms. He has received several awards for his research including a best paper award by Journal of Global Optimization in 2021 and the Columbia-Willamette Chapter of Sigma Xi Outstanding Researcher Award in Mathematical Sciences in 2015. His research was supported by grants from the National Science Foundation, the Simons Foundation, and Portland State University.
Zusammenfassung

Presents a unified theory of convex analysis, optimization, and related topics in both finite and infinite dimensions

Highlights a variational approach to convex analysis and applications

Includes in-text exercises and figures suitable for graduate and undergraduate coursework

Inhaltsverzeichnis

Fundamentals.- Basic theory of convexity.- Convex generalized differentiation.- Enhanced calculus and fenchel duality.- Variational techniques and further subgradient study.- Miscellaneous topics on convexity.- Convexified Lipschitzian analysis.- List of Figures.- Glossary of Notation and Acronyms.- Subject Index.

Details
Erscheinungsjahr: 2022
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Springer Series in Operations Research and Financial Engineering
Inhalt: xvii
585 S.
7 s/w Illustr.
40 farbige Illustr.
585 p. 47 illus.
40 illus. in color.
ISBN-13: 9783030947842
ISBN-10: 303094784X
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Mau Nam, Nguyen
Mordukhovich, Boris S.
Auflage: 1st ed. 2022
Hersteller: Springer International Publishing
Springer International Publishing AG
Springer Series in Operations Research and Financial Engineering
Maße: 241 x 160 x 36 mm
Von/Mit: Nguyen Mau Nam (u. a.)
Erscheinungsdatum: 25.04.2022
Gewicht: 1,172 kg
Artikel-ID: 120919877
Über den Autor
Boris Mordukhovich is Distinguished University Professor of Mathematics at Wayne State University. He has more than 500 publications including several monographs. Among his best known achievements are the introduction and development of powerful constructions of generalized differentiation and their applications to broad classes of problems in variational analysis, optimization, equilibrium, control, economics, engineering, and other fields. Mordukhovich is a SIAM Fellow, an AMS Fellow, and a recipient of many international awards and honors including Doctor Honoris Causa degrees from six universities over the world. He is a Highly Cited Researcher in Mathematics. His research has been supported by continued grants from the National Science Foundations and the Air Force Office of Scientific Research.
Nguyen Mau Nam is a Professor of Mathematics at Portland State University. He has published more than 55 research articles and one book in convex analysis withapplications to optimization theory and numerical algorithms. He has received several awards for his research including a best paper award by Journal of Global Optimization in 2021 and the Columbia-Willamette Chapter of Sigma Xi Outstanding Researcher Award in Mathematical Sciences in 2015. His research was supported by grants from the National Science Foundation, the Simons Foundation, and Portland State University.
Zusammenfassung

Presents a unified theory of convex analysis, optimization, and related topics in both finite and infinite dimensions

Highlights a variational approach to convex analysis and applications

Includes in-text exercises and figures suitable for graduate and undergraduate coursework

Inhaltsverzeichnis

Fundamentals.- Basic theory of convexity.- Convex generalized differentiation.- Enhanced calculus and fenchel duality.- Variational techniques and further subgradient study.- Miscellaneous topics on convexity.- Convexified Lipschitzian analysis.- List of Figures.- Glossary of Notation and Acronyms.- Subject Index.

Details
Erscheinungsjahr: 2022
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Springer Series in Operations Research and Financial Engineering
Inhalt: xvii
585 S.
7 s/w Illustr.
40 farbige Illustr.
585 p. 47 illus.
40 illus. in color.
ISBN-13: 9783030947842
ISBN-10: 303094784X
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Mau Nam, Nguyen
Mordukhovich, Boris S.
Auflage: 1st ed. 2022
Hersteller: Springer International Publishing
Springer International Publishing AG
Springer Series in Operations Research and Financial Engineering
Maße: 241 x 160 x 36 mm
Von/Mit: Nguyen Mau Nam (u. a.)
Erscheinungsdatum: 25.04.2022
Gewicht: 1,172 kg
Artikel-ID: 120919877
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