Practical Mathematical Optimization
Basic Optimization Theory and Gradient-Based Algorithms
Authors: Snyman, Jan A, Wilke, Daniel N
Free Preview- 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
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- About this Textbook
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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.
- About the authors
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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, mathematical programming 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.
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- Table of contents (9 chapters)
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INTRODUCTION
Pages 3-40
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LINE SEARCH DESCENT METHODS FOR UNCONSTRAINED MINIMIZATION
Pages 41-69
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STANDARD METHODS FOR CONSTRAINED OPTIMIZATION
Pages 71-112
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BASIC EXAMPLE PROBLEMS
Pages 113-167
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SOME BASIC OPTIMIZATION THEOREMS
Pages 169-193
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Table of contents (9 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Practical Mathematical Optimization
- Book Subtitle
- Basic Optimization Theory and Gradient-Based Algorithms
- Authors
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- Jan A Snyman
- Daniel N Wilke
- Series Title
- Springer Optimization and Its Applications
- Series Volume
- 133
- Copyright
- 2018
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing AG, part of Springer Nature
- eBook ISBN
- 978-3-319-77586-9
- DOI
- 10.1007/978-3-319-77586-9
- Hardcover ISBN
- 978-3-319-77585-2
- Series ISSN
- 1931-6828
- Edition Number
- 2
- Number of Pages
- XXVI, 372
- Number of Illustrations
- 64 b/w illustrations, 17 illustrations in colour
- Topics
