Introduction to the Theory of Nonlinear Optimization

Fourth Auflage 2020
ISBN: 978-3-030-42762-7
Verlag: Springer International Publishing

Buch, Englisch, 323 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 511 g

This book offers an introduction to optimization theory in normed spaces. The topics covered include existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and an investigation of linear quadratic and time minimal control problems. The 4 edition of this book has been extensively revised and a new chapter on discrete-continuous optimization has been added. This textbook focuses on the fundamentals, with particular emphasis on their application to problems in the calculus of variations, approximation and optimal control theory. The reader is assumed to have a basic grasp of linear functional analysis.

Zielgruppe

Graduate

Autoren/Hrsg.

Jahn, Johannes

Fachgebiete

• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung

Inhaltsverzeichnis

Introduction and Problem Formulation.- Existence Theorems for Minimal Points.- Generalized Derivatives.- Tangent Cones.- Generalized Lagrange Multiplier Rule.- Duality.- Application to Extended Semidefinite Optimization.- Extension to Discrete-Continuous Problems.- Direct Treatment of Special Optimization Problems.

Über Autor(innen)

Johannes Jahn is professor emeritus at the Department of Mathematics of the University of Erlangen-Nürnberg (Germany). His research interests are theory and numerical methods in nonlinear optimization, vector optimization and set optimization. Johannes Jahn is the editor of the book series on "Vector Optimization" published with Springer.