國立高雄大學圖資館 |

Language: English

Back

Convex analysis and beyond.Volume I,Basic theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Convex analysis and beyond.by Boris S. Mordukhovich, Nguyen Mau Nam.
remainder title:	Basic theory
Author:	Mordukhovich, B. Sh.
other author:	Mau Nam, Nguyen.
Published:	Cham :Springer International Publishing :2022.
Description:	xvii, 585 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Convex geometry.
Online resource:	https://doi.org/10.1007/978-3-030-94785-9
ISBN:	9783030947859$q(electronic bk.)

Convex analysis and beyond.Volume I,Basic theory
Mordukhovich, B. Sh.

Convex analysis and beyond.Volume I,Basic theory[electronic resource] /Basic theoryby Boris S. Mordukhovich, Nguyen Mau Nam. - Cham :Springer International Publishing :2022. - xvii, 585 p. :ill., digital ;24 cm. - Springer series in operations research and financial engineering,2197-1773. - Springer series in operations research and financial engineering..

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.

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.

ISBN: 9783030947859$q(electronic bk.)

Standard No.: 10.1007/978-3-030-94785-9doiSubjects--Topical Terms:

187435
Convex geometry.

LC Class. No.: QA639.5 / .M67 2022

Dewey Class. No.: 516.08

Convex analysis and beyond.Volume I,Basic theory
LDR:02896nmm a2200349 a 4500 001 621428
003 DE-He213
005 20220424050441.0
006 m d
007 cr nn 008maaau
008 221121s2022 sz s 0 eng d
020 $a 9783030947859$q(electronic bk.)
020 $a 9783030947842$q(paper)
024 7 $a 10.1007/978-3-030-94785-9 $2 doi
035 $a 978-3-030-94785-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA639.5 $b .M67 2022
072 7 $a PBU $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PBU $2 thema
082 0 4 $a 516.08 $2 23
090 $a QA639.5 $b .M834 2022
100 1 $a Mordukhovich, B. Sh. $3 922621
245 1 0 $a Convex analysis and beyond. $n Volume I, $p Basic theory $h [electronic resource] / $c by Boris S. Mordukhovich, Nguyen Mau Nam.
246 3 0 $a Basic theory
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xvii, 585 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer series in operations research and financial engineering, $x 2197-1773
505 0 $a 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.
520 $a 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.
650 0 $a Convex geometry. $3 187435
650 0 $a Convex functions. $3 191128
650 1 4 $a Optimization. $3 274084
650 2 4 $a Numerical Analysis. $3 275681
700 1 $a Mau Nam, Nguyen. $3 922622
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Springer series in operations research and financial engineering. $3 567467
856 4 0 $u https://doi.org/10.1007/978-3-030-94785-9
950 $a Mathematics and Statistics (SpringerNature-11649)