Springer Series in Operations Research and Financial Engineering Ser.: Convex...

Convex Analysis and BeyondVolume I: Basic Theory\nAuthor(s): Boris S. Mordukhovich, Nguyen Mau Nam\nFormat: Hardback\nPublisher: Springer Nature Switzerland AG, Switzerland\nImprint: Springer Nature Switzerland AG\nISBN-13: 9783030947842, 978-3030947842\nSynopsis\nThis 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 de.