Overview
- Guides readers to understand processes and strategies in real world optimization problems
- Contains new material on gradient-based methods, algorithm implementation via Python, and basic optimization principles
- Covers fundamental optimization concepts and definitions, search techniques for unconstrained minimization and standard methods for constrained optimization
- Includes example problems and exercises
Part of the book series: Springer Optimization and Its Applications (SOIA, volume 133)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (9 chapters)
-
Front Matter
-
Basic optimization theory
-
Front Matter
-
-
Gradient-based algorithms
-
Front Matter
-
-
Back Matter
Keywords
- Mathematica
- algorithms
- linear optimization
- optimization
- programming
- Python
- multi-modal optimization
- non-smooth optimization
- discontinuous optimization
- Numerical Linear Algebra
- Hessian matrix approximations
- Gradient-only solution strategies
- Karush-Kuhn-Tucker theory
- Quadratic programming
- line search descent algorithm for unconstrained minimization
- Unconstrained one-dimensional minimization
About this book
This textbook presents a wide range of tools for a course in mathematical optimization for upper undergraduate and graduate students in mathematics, engineering, computer science, and other applied sciences. Basic optimization principles are presented with emphasis on gradient-based numerical optimization strategies and algorithms for solving both smooth and noisy discontinuous optimization problems. Attention is also paid to the difficulties of expense of function evaluations and the existence of multiple minima that often unnecessarily inhibit the use of gradient-based methods. This second edition addresses further advancements of gradient-only optimization strategies to handle discontinuities in objective functions. New chapters discuss the construction of surrogate models as well as new gradient-only solution strategies and numerical optimization using Python. A special Python module is electronically available (via springerlink) that makes the new algorithms featured in the text easily accessible and directly applicable. Numerical examples and exercises are included to encourage senior- to graduate-level students to plan, execute, and reflect on numerical investigations. By gaining a deep understanding of the conceptual material presented, students, scientists, and engineers will be able to develop systematic and scientific numerical investigative skills.
Authors and Affiliations
About the authors
Jan A. Snyman currently holds the position of emeritus professor in the Department of Mechanical and Aeronautical Engineering of the University of Pretoria, having retired as full professor in 2005. He has taught physics, mathematics and engineering mechanics to science and engineering students at undergraduate and postgraduate level, and has supervised the theses of 26 Masters and 8 PhD students. His research mainly concerns the development of gradient-based trajectory optimization algorithms for solving noisy and multi-modal problems, and their application in approximation methodologies for the optimal design of engineering systems. He has authored or co-authored 89 research articles in peer-reviewed journals as well as numerous papers in international conference proceedings.
Daniel N. Wilke is a senior lecturer in the Department of Mechanical and Aeronautical Engineering of the University of Pretoria. He teaches computer programming, mathematicalprogramming and computational mechanics to science and engineering students at undergraduate and postgraduate level. His current research focuses on the development of interactive design optimization technologies, and enabling statistical learning (artificial intelligence) application layers, for industrial processes and engineering design. He has co-authored over 50 peer-reviewed journal articles and full length conference papers.
Bibliographic Information
Book Title: Practical Mathematical Optimization
Book Subtitle: Basic Optimization Theory and Gradient-Based Algorithms
Authors: Jan A Snyman, Daniel N Wilke
Series Title: Springer Optimization and Its Applications
DOI: https://doi.org/10.1007/978-3-319-77586-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-77585-2Published: 14 May 2018
Softcover ISBN: 978-3-030-08486-8Published: 10 January 2019
eBook ISBN: 978-3-319-77586-9Published: 02 May 2018
Series ISSN: 1931-6828
Series E-ISSN: 1931-6836
Edition Number: 2
Number of Pages: XXVI, 372
Number of Illustrations: 64 b/w illustrations, 17 illustrations in colour
Topics: Optimization, Algorithms, Operations Research, Management Science, Numerical Analysis, Mathematical Software, Real Functions