An Easy Path to Convex Analysis and Applications

Boris Mordukhovich, Nguyen Mau Nam (Autoren)

Buch | Softcover

XX, 300 Seiten

2024 | 2nd ed. 2023
Springer International Publishing (Verlag)
978-3-031-26460-3 (ISBN)

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This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and to build a theory of generalized differentiation for convex functions and sets in finite dimensions. The book serves as a bridge for the readers who have just started using convex analysis to reach deeper topics in the field. Detailed proofs are presented for most of the results in the book and also included are many figures and exercises for better understanding the material. Applications provided include both the classical topics of convex optimization and important problems of modern convex optimization, convex geometry, and facility location.

Boris Mordukhovich, PhD, 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. Dr. 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, PhD, is Professor of Mathematics at Portland State University. He has published more than 60 research articles and one book in convex analysiswith 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.

Convex Sets and Functions.- Convex Separation and Some Consequences.- Convex Generalized Differentiation.- Fenchel Conjugate and Further Topics In Subdifferentiation.- Remarkable Consequences of Convexity.- Minimal Time Functions and Related Issues.- Applications To Problems of Optimization and Equilibrium.- Applications To Location Problems.

Erscheinungsdatum	22.05.2024
Reihe/Serie	Synthesis Lectures on Mathematics & Statistics
Zusatzinfo	XX, 300 p. 35 illus., 31 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	168 x 240 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Convex Analysis and Optimization • convex function • convex set • Facility Location • Fenchel conjugate • Generalized differentiation
ISBN-10	3-031-26460-6 / 3031264606
ISBN-13	978-3-031-26460-3 / 9783031264603
Zustand	Neuware