Springer Optimization and Its Applications

Nonlinear Conjugate Gradient Methods for Unconstrained Optimization

Authors: Neculai, Andrei

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  • An explicit and thorough treatment of the conjugate gradient algorithms for unconstrained optimization properties and convergence
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  • A clear illustration of the numerical performances of the algorithms described in the book
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  • Provides a deep analysis of the performances of the algorithms
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  • Maximizes the reader’s insight into the implementation of the conjugate gradient methods in professional computing programs
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  • ISBN 978-3-030-42950-8
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Hardcover $149.99
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About this book

Two approaches are known for solving large-scale unconstrained optimization problems—the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given.  

The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000].  The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex 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 students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.


About the authors

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 2 books with Springer including Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology (2017) and Nonlinear Optimization Applications Using the GAMS Technology (2013).

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-030-42950-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover $149.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Conjugate Gradient Methods for Unconstrained Optimization
Authors
Series Title
Springer Optimization and Its Applications
Series Volume
158
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-42950-8
DOI
10.1007/978-3-030-42950-8
Hardcover ISBN
978-3-030-42949-2
Series ISSN
1931-6828
Edition Number
1
Number of Pages
XXVIII, 498
Number of Illustrations
3 b/w illustrations, 90 illustrations in colour
Topics