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Introduction to the Theory of Nonlinear Optimization

  • Book
  • © 2007

Overview

Authors:
  1. Johannes Jahn

    1. Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

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  • Third edition of standard text

  • Covers all areas of nonlinear optimization, particular emphasis on applications

  • Includes supplementary material: sn.pub/extras

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction and Problem Formulation

    Pages 1-5

  3. Existence Theorems for Minimal Points

    Pages 7-30

  4. Generalized Derivatives

    Pages 31-77

  5. Tangent Cones

    Pages 79-104

  6. Generalized Lagrange Multiplier Rule

    Pages 105-158

  7. Duality

    Pages 159-185

  8. Application to Extended Semidefinite Optimization

    Pages 187-211

  9. Direct Treatment of Special Optimization Problems

    Pages 213-240

  10. Back Matter

    Pages 241-292
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Keywords

About this book

This book serves as an introductory text to optimization theory in normed spaces. Topics of this book are 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 the investigation of linear quadratic and time minimal control problems. This textbook presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.

Reviews

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)

Authors and Affiliations

  • Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

    Johannes Jahn

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