Fundamentals of Convex Analysis and Optimization

• Verfasst von: Correa, Rafael [VerfasserIn]
• Verfasst von: Hantoute, Abderrahim [VerfasserIn]
• Verfasst von: López, Marco A. [VerfasserIn]
• Titel: Fundamentals of Convex Analysis and Optimization
• Titelzusatz: A Supremum Function Approach
• Verf.angabe: by Rafael Correa, Abderrahim Hantoute, Marco A. López
• Verlagsort: Cham
• Verlag: Springer
• Jahr: 2023
• Umfang: 1 Online-Ressource (XIII, 444 p. 1 illus.)
• Gesamttitel/Reihe: Springer Series in Operations Research and Financial Engineering
• ISBN: 978-3-031-29551-5
• DOI: doi:10.1007/978-3-031-29551-5
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Correa, Rafael: Fundamentals of convex analysis and optimization. - Cham : Springer, 2023. - xiii, 444 Seiten
• K10plus-PPN: 1852903198
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

1. Introduction -- 2. Preliminaries -- 3. Fenchel-Moreau-Rockafellar theory -- 4. Fundamental topics in convex analysis -- 5. Supremum of convex functions -- 6. The supremum in specific contexts -- 7. Other subdifferential calculus rules -- 8. Miscellaneous -- 9. Exercises - Solutions -- Index -- Glossary of Notations -- Bibliography.

Abstract

This book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, and the study of Chebychev sets. At the same time, the underlying geometrical meaning of all the involved concepts and operations is highlighted and duly emphasized. A notable feature of the book is its unifying methodology, as well as the novelty of providing an alternative or complementary view to the traditional one in which the discipline is presented to students and researchers. This textbook can be used for courses on optimization, convex and variational analysis, addressed to graduate and post-graduate students of mathematics, and also students of economics and engineering. It is also oriented to provide specific background for courses on optimal control, data science, operations research, economics (game theory), etc. The book represents a challenging and motivating development for those experts in functional analysis, convex geometry, and any kind of researchers who may be interested in applications of their work.