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  • © 2018

Practical Mathematical Optimization

Basic Optimization Theory and Gradient-Based Algorithms

  • 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)

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  • ISBN: 978-3-319-77586-9
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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxvi
  2. Basic optimization theory

    1. Front Matter

      Pages 1-1
    2. INTRODUCTION

      • Jan A. Snyman, Daniel N. Wilke
      Pages 3-40
    3. LINE SEARCH DESCENT METHODS FOR UNCONSTRAINED MINIMIZATION

      • Jan A. Snyman, Daniel N. Wilke
      Pages 41-69
    4. STANDARD METHODS FOR CONSTRAINED OPTIMIZATION

      • Jan A. Snyman, Daniel N. Wilke
      Pages 71-112
    5. BASIC EXAMPLE PROBLEMS

      • Jan A. Snyman, Daniel N. Wilke
      Pages 113-167
    6. SOME BASIC OPTIMIZATION THEOREMS

      • Jan A. Snyman, Daniel N. Wilke
      Pages 169-193
  3. Gradient-based algorithms

    1. Front Matter

      Pages 195-195
    2. NEW GRADIENT-BASED TRAJECTORY AND APPROXIMATION METHODS

      • Jan A. Snyman, Daniel N. Wilke
      Pages 197-250
    3. SURROGATE MODELS

      • Jan A. Snyman, Daniel N. Wilke
      Pages 251-271
    4. GRADIENT-ONLY SOLUTION STRATEGIES

      • Jan A. Snyman, Daniel N. Wilke
      Pages 273-310
    5. PRACTICAL COMPUTATIONAL OPTIMIZATION USING PYTHON

      • Jan A. Snyman, Daniel N. Wilke
      Pages 311-340
  4. Back Matter

    Pages 341-372

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.

 

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

Authors and Affiliations

  • Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, South Africa

    Jan A Snyman, Daniel N Wilke

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, 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.

Bibliographic Information

Buying options

eBook USD 79.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-77586-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 99.99
Price excludes VAT (USA)
Hardcover Book USD 99.99
Price excludes VAT (USA)