Convex Analysis and Beyond
Volume I: Basic Theory
Series: Springer Series in Operations Research and Financial Engineering;
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Product details:
- Edition number 1st ed. 2022
- Publisher Springer
- Date of Publication 25 April 2023
- Number of Volumes 1 pieces, Book
- ISBN 9783030947873
- Binding Paperback
- No. of pages585 pages
- Size 235x155 mm
- Weight 1070 g
- Language English
- Illustrations 7 Illustrations, black & white; 40 Illustrations, color 506
Categories
Short description:
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.
Long description:
?Each chapter ends with an exercise section ? . While primarily addressed to researchers, the book can be used for graduate courses in optimization, by undergraduate and graduate students for theses and projects as well as by researchers and practitioners from other fields where tools from convex analysis, variational analysis and optimization play a role. All in one, the reviewer warmly recommends this book to anyone interested.? (Sorin-Mihai Grad, zbMATH 1506.90001, 2023)
?Every chapter of the book has one section of exercises and one section of commentaries. These sections provide the reader with a lot of information and give him/her great benefits in self-learning. ? The book under review has many things to offer and, surely, it will play an important role in the development of convex analysis ? . The book is very useful for theoretical research and practical use. Thanks to the art of writing of the authors ? .? (Nguyen Dong Yen, Journal of Global Optimization, Vol. 85, 2023)
Table of Contents:
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.
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