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Introduction to the Theory of Nonlinear Optimization

  • Textbook
  • © 2020

Overview

Authors:
  1. Johannes Jahn

    1. Department of Mathematics, University of Erlangen-Nürnberg, Erlangen, Germany

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  • The extensively revised fourth edition of a standard work in its field

  • Covers important areas of nonlinear optimization with particular emphasis on their applications

  • Includes a new chapter on discrete-continuous optimization

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction and Problem Formulation

    • Johannes Jahn
    Pages 1-7

  3. Existence Theorems for Minimal Points

    • Johannes Jahn
    Pages 9-32

  4. Generalized Derivatives

    • Johannes Jahn
    Pages 33-77

  5. Tangent Cones

    • Johannes Jahn
    Pages 79-106

  6. Generalized Lagrange Multiplier Rule

    • Johannes Jahn
    Pages 107-159

  7. Duality

    • Johannes Jahn
    Pages 161-188

  8. Application to Extended Semidefinite Optimization

    • Johannes Jahn
    Pages 189-211

  9. Extension to Discrete-Continuous Problems

    • Johannes Jahn
    Pages 213-251

  10. Direct Treatment of Special Optimization Problems

    • Johannes Jahn
    Pages 253-280

  11. Back Matter

    Pages 281-323
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Erlangen-Nürnberg, Erlangen, Germany

    Johannes Jahn

About the author

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.

Bibliographic Information

  • Book Title: Introduction to the Theory of Nonlinear Optimization

  • Authors: Johannes Jahn

  • DOI: https://doi.org/10.1007/978-3-030-42760-3

  • Publisher: Springer Cham

  • eBook Packages: Business and Management, Business and Management (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-42759-7Published: 03 July 2020

  • Softcover ISBN: 978-3-030-42762-7Published: 03 July 2021

  • eBook ISBN: 978-3-030-42760-3Published: 02 July 2020

  • Edition Number: 4

  • Number of Pages: X, 323

  • Number of Illustrations: 51 b/w illustrations

  • Topics: Operations Research/Decision Theory, Optimization, Computational Intelligence

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