Johannes Jahn

Introduction to the Theory of Nonlinear Optimization

• Gebundenes Buch

Produktbeschreibung

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 4th 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.

Produktdetails

• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-030-42759-7
• 4. Aufl.
• Seitenzahl: 336
• Erscheinungstermin: 3. Juli 2020
• Englisch
• Abmessung: 241mm x 160mm x 24mm
• Gewicht: 650g
• ISBN-13: 9783030427597
• ISBN-10: 3030427595
• Artikelnr.: 58597784

Autorenporträt

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.

Inhaltsangabe

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.

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

Rezensionen

From the reviews of the third edition:

"Jahn's textbook provides a thorough development of optimality conditions for optimization problems on function spaces. ... The book will be of interest to suitably prepared graduate students and researchers who are working on problems in optimal control theory. It may also be of interest to analysts who want to learn something about how functional analysis is used in the theory of optimization." (Brain Borchers, MathDL, April, 2007)

"The third edition of this book has eight chapters ... . The book is written in a lucid style. It may be very useful to lecturers, students, and researchers." (Stanislaw Walczak, Zentralblatt MATH, Vol. 1115 (17), 2007)