Convex Analysis and Beyond: Volume I: Basic Theory (Springer Series in Operations Research and Financial Engineering)

Mordukhovich, Boris S.; Mau Nam, Nguyen

ISBN 10: 3030947874 / ISBN 13: 9783030947873

Editore: Springer, 2023

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1st ed. 2022 edition NO-PA16APR2015-KAP. Codice articolo 26396290417

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Titolo: Convex Analysis and Beyond: Volume I: Basic ...

Casa editrice: Springer

Data di pubblicazione: 2023

Legatura: Brossura

Condizione: New

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Riassunto:

This book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specitions to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which des on set extremality with its characterizations and specitions 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 urce to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.