Convex Analysis and Beyond

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 with applications 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.

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.

"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)
"This outstanding book will certainly be useful to anyone interested to learn convex analysis, in particular to graduate students and researchers in the field. Most parts of it can also serve as the basis of advanced courses on a variety of topics. In view of the excellence of this first volume, one can expect the best of the announced second one, which will deal with applications of convex analysis." (Juan Enrique Martínez-Legaz, Mathematical Reviews, February, 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)