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Practical Mathematical Optimization

An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms

  • Textbook
  • © 2005

Overview

Authors:
  1. Jan A. Snyman

    1. University of Pretoria, Pretoria, South Africa

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  • Presents the theory in a straightforward readable manner
  • This is the first compact reference to address difficulties that inhibit broad use of gradient-based methods
  • Shows how to apply optimization theory and algorithms in such fields as engineering, physics, chemistry, or business economics
  • Includes theorems of particular interest and many worked-out example problems
  • Includes supplementary material: sn.pub/extras

Part of the book series: Applied Optimization (APOP, volume 97)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xx
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  2. Introduction

    Pages 1-32

  3. Line Search Descent Methods for Unconstrained Minimization

    Pages 33-55

  4. Standard Methods for Constrained Optimization

    Pages 57-96

  5. New Gradient-Based Trajectory and Approximation Methods

    Pages 97-150

  6. Example Problems

    Pages 151-205

  7. Some Theorems

    Pages 207-231

  8. Back Matter

    Pages 233-257
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Keywords

About this book

It is intended that this book be used in senior- to graduate-level semester courses in optimization, as offered in mathematics, engineering, com­ puter science and operations research departments. Hopefully this book will also be useful to practising professionals in the workplace. The contents of the book represent the fundamental optimization mate­ rial collected and used by the author, over a period of more than twenty years, in teaching Practical Mathematical Optimization to undergradu­ ate as well as graduate engineering and science students at the University of Pretoria. The principal motivation for writing this work has not been the teaching of mathematics per se, but to equip students with the nec­ essary fundamental optimization theory and algorithms, so as to enable them to solve practical problems in their own particular principal fields of interest, be it physics, chemistry, engineering design or business eco­ nomics. The particular approach adopted here follows from the author's own personal experiences in doing research in solid-state physics and in mechanical engineering design, where he was constantly confronted by problems that can most easily and directly be solved via the judicious use of mathematical optimization techniques. This book is, however, not a collection of case studies restricted to the above-mentioned specialized research areas, but is intended to convey the basic optimization princi­ ples and algorithms to a general audience in such a way that, hopefully, the application to their own practical areas of interest will be relatively simple and straightforward.

Authors and Affiliations

  • University of Pretoria, Pretoria, South Africa

    Jan A. Snyman

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