An Easy Path to Convex Analysis and Applic...

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

Explains the fundamental theory with an accessible and understandable variational geometric approach

Provides easy access to theoretical and numerical applications to convex optimization and geometry

Simplifies relative interiors when developing the theory of generalized differentiation in finite dimensions

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2023
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Synthesis Lectures on Mathematics & Statistics
Inhalt:	xx 300 S. 4 s/w Illustr. 31 farbige Illustr. 300 p. 35 illus. 31 illus. in color.
ISBN-13:	9783031264573
ISBN-10:	3031264576
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Nam, Nguyen Mau Mordukhovich, Boris
Auflage:	2nd ed. 2023
Hersteller:	Springer International Publishing Springer International Publishing AG Synthesis Lectures on Mathematics & Statistics
Maße:	246 x 173 x 23 mm
Von/Mit:	Nguyen Mau Nam (u. a.)
Erscheinungsdatum:	16.05.2023
Gewicht:	0,715 kg

Artikel-ID: 126446227