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Modern Numerical Nonlinear Optimization

  • Book
  • © 2022

Overview

Authors:
  1. Neculai Andrei

    1. Academy of Romanian Scientists, Center for Advanced Modeling and Optimization, Bucharest, Romania

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  • Nonlinear optimization algorithms for solving large-scale unconstrained and constrained optimization applications
  • Optimization methods that are currently the most valuable for solving real-life problems and applications
  • Provides theoretical background which gives insights into how the methods are derived

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 195)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xxxiii
    Download chapter PDF

  2. Introduction

    • Neculai Andrei
    Pages 1-19

  3. Fundamentals on Unconstrained Optimization. Stepsize Computation

    • Neculai Andrei
    Pages 21-80

  4. Steepest Descent Methods

    • Neculai Andrei
    Pages 81-107

  5. The Newton Method

    • Neculai Andrei
    Pages 109-168

  6. Conjugate Gradient Methods

    • Neculai Andrei
    Pages 169-260

  7. Quasi-Newton Methods

    • Neculai Andrei
    Pages 261-314

  8. Inexact Newton Methods

    • Neculai Andrei
    Pages 315-330

  9. The Trust-Region Method

    • Neculai Andrei
    Pages 331-353

  10. Direct Methods for Unconstrained Optimization

    • Neculai Andrei
    Pages 355-370

  11. Constrained Nonlinear Optimization Methods: An Overview

    • Neculai Andrei
    Pages 371-382

  12. Optimality Conditions for Nonlinear Optimization

    • Neculai Andrei
    Pages 383-409

  13. Simple Bound Constrained Optimization

    • Neculai Andrei
    Pages 411-437

  14. Quadratic Programming

    • Neculai Andrei
    Pages 439-474

  15. Penalty and Augmented Lagrangian Methods

    • Neculai Andrei
    Pages 475-519

  16. Sequential Quadratic Programming

    • Neculai Andrei
    Pages 521-567

  17. Primal Methods: The Generalized Reduced Gradient with Sequential Linearization

    • Neculai Andrei
    Pages 569-597

  18. Interior-Point Methods

    • Neculai Andrei
    Pages 599-645

  19. Filter Methods

    • Neculai Andrei
    Pages 647-659

  20. Interior-Point Filter Line-Search

    • Neculai Andrei
    Pages 661-678
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Keywords

About this book

This book includes a thorough theoretical and computational analysis of unconstrained and constrained optimization algorithms and combines and integrates the most recent techniques and advanced computational linear algebra methods. Nonlinear optimization methods and techniques have reached their maturity and an abundance of optimization algorithms are available for which both the convergence properties and the numerical performances are known. This clear, friendly, and rigorous exposition discusses the theory behind the nonlinear optimization algorithms for understanding their properties and their convergence, enabling the reader to prove the convergence of his/her own algorithms. It covers cases and computational performances of the most known modern nonlinear optimization algorithms that solve collections of unconstrained and constrained optimization test problems with different structures, complexities, as well as those with large-scale real applications.

The book is addressed to all those interested in developing and using new advanced techniques for solving large-scale unconstrained or constrained complex optimization problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master in mathematical programming will find plenty of recent information and practical approaches for solving real large-scale optimization problems and applications.

Reviews

“This book gives a comprehensive description of the theoretical details and the computational performance of the modern optimization algorithms for solving … different areas of activity. … I think this book has the following two features. First, it emphasizes and illustrates a number of reliable and robust packages for solving … nonlinear optimization problems and applications. Second, the text is well illustrated with drawings and numerical studies of many large-scale test problems, which significantly increase the readability of the book.” (Xiaoliang Dong, Mathematical Reviews, September, 2023)

Authors and Affiliations

  • Academy of Romanian Scientists, Center for Advanced Modeling and Optimization, Bucharest, Romania

    Neculai Andrei

About the author

Neculai Andrei holds a position at the Center for Advanced Modeling and Optimization at the Academy of Romanian Scientists in Bucharest, Romania. Dr. Andrei’s areas of interest include mathematical modeling, linear programming, nonlinear optimization, high performance computing, and numerical methods in mathematical programming. In addition to this present volume, Neculai Andrei has published several books with Springer including A Derivative-free Two Level Random Search Method for Unconstrained Optimization (2021), Nonlinear Conjugate Gradient Methods for Unconstrained Optimization (2020), Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology (2017), and Nonlinear Optimization Applications Using the GAMS Technology (2013).

Bibliographic Information

  • Book Title: Modern Numerical Nonlinear Optimization

  • Authors: Neculai Andrei

  • Series Title: Springer Optimization and Its Applications

  • DOI: https://doi.org/10.1007/978-3-031-08720-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-031-08719-6Published: 19 October 2022

  • Softcover ISBN: 978-3-031-08722-6Published: 19 October 2023

  • eBook ISBN: 978-3-031-08720-2Published: 18 October 2022

  • Series ISSN: 1931-6828

  • Series E-ISSN: 1931-6836

  • Edition Number: 1

  • Number of Pages: XXXIII, 807

  • Number of Illustrations: 9 b/w illustrations, 108 illustrations in colour

  • Topics: Optimization, Computational Mathematics and Numerical Analysis, Algorithms

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