Global Optimization with Maple
An Introduction with Illustrative Examples

--- An interactive electronic book ---

Written by János D. Pintér

Published and distributed by Pintér Consulting Services Inc., Halifax, NS, Canada and Maplesoft, a division of Waterloo Maple Inc.
Waterloo, ON, Canada

© Pintér Consulting Services Inc., 2006,  ISBN 1-897310-15-3

Electronic version available by download (from  Maplesoft) or by e-mail (from the author).

Single user price: USD 99.00; group and site licenses are also available.

Please contact the author
<jdpinter@hfx.eastlink.ca> or Maplesoft <info@maplesoft.com> for further details.


Summary Description

This (approximately 150-page when printed)  electronic book presents Maple as an advanced  model development and optimization environment. A special emphasis is placed on solving  multiextremal models, using the Global  Optimization ToolboxT for MapleT. Following a
brief topical introduction, an extensive collection of detailed numerical examples and illustrative case studies is presented. The book
is available in the form of a fully functional  (interactive, readily modifiable), printable Maple worksheet, and/or as a set of hyperlinked
worksheets. This live book works with Maple 9.5  or above, across all supported Maple platforms.  To solve the models presented in the book, the Global Optimization Toolbox is recommended, and it is used throughout the book. Readers may also like to experiment with built-in Maple
optimization functionality, or perhaps with their own native Maple solvers.

The Global Optimization Toolbox is available from Maplesoft
http://www.maplesoft.com/products/toolboxes/globaloptimization/.
Please feel free to contact the author
<jdpinter@hfx.eastlink.ca> for technical information and background.

The following topics are covered (please see TOC below for details):

* A brief introduction to Operations Research / Management Science (ORMS)
* Maple as an integrated platform for developing ORMS studies and applications
* A review of the key global optimization concepts
* The Global Optimization ToolboxT (GOT) for
MapleT, including a concise discussion of the core LGOT solver technology
* Model development tips
* Detailed "hands-on" numerical examples of using
the GOT, from a simple illustration of the key
tools and options to more advanced challenges
* Illustrative case studies from the sciences and engineering.

This electronic book will be of interest to
practitioners, researchers, academics and
students in the quantitative sciences and engineering.


Table of Contents

Preface
Acknowledgements
About the Author

Chapter 1: Introduction and Background
1.1   Operations Research for Decision Analysis and Support
1.2   Developing Decision Support Applications in Maple
1.3   Global Optimization: Relevance and Key Concepts
1.4   The LGO Solver Suite for Global and Local Optimization

Chapter 2: Global Optimization Toolbox for Maple
2.1   The Global Optimization Toolbox
2.2   Toolbox Installation
2.3   Initializing the GlobalOptimization and Optimization Packages
2.4   GOT Options and Parameter Settings
2.5   Model Formulation and Function Evaluation Options
2.6.  Global Optimization: Model Development and Solver Suggestions

Chapter 3: Getting Started with the GOT
3.1   A Convex Model
3.2   A Nonconvex Model
3.3   Runtime Information Level Options
3.4   A Difficult One-Dimensional Example, and a Cautionary Note
3.5   A "Standard" Model Development and Solution Approach
3.6   Shubert's Test Problem with Added Constraints
3.7   Standard Box-Constrained Nonlinear Optimization Test Problems
3.8   Some More Challenging Box-Constrained Models
3.9   Constrained Optimization Test Models
3.10   Incremental Model Development: An Example
3.11   Scalable Test Models
3.12   Model Definition by Procedural (Matrix) Formulation
3.13   A Linear Optimization Model with Indexed Variables
3.14   A Nonlinear Model with Indexed Variables
3.15   Using the GOT in Interactive Mode: A Box-Constrained Example
3.16   A General Constrained Model Solved in Interactive Mode
3.17   The GOT in Interactive Mode: Further Examples

Chapter 4: More Advanced Examples
4.1   Trefethen's Hundred-dollar, Hundred-digit Challenge: Problem 4
4.2   Optimization with Embedded Computable
Functions: An Example with Gamma Function
4.3   Optimization with Embedded Computable
Functions: Examples with Trigonometric and Psi Functions
4.4   Optimization with Embedded Computable
Functions: An Example with Bessel Functions
4.5   Optimization with Embedded Computable
Functions: An Example with Spline Interpolation
4.6   Optimization of a Parametric Integral (Trefethen's Problem 9)
4.7   Calling MATLAB to Define Model Functions
4.8   Using External (Precompiled) Functions in a Model
4.9   Reporting the Current Best Solution from a
Numerical Procedure During Optimization

Chapter 5: Illustrative Case Studies
5.1   Systems of Nonlinear Equations
5.2   A Simple Manufacturing Design Problem
5.3   A Model Fitting Example
5.4   A More Difficult Model Calibration Problem
5.5   A Chemical Equilibrium Model
5.6   Alkylation Process Model
5.7   Circuit Design Problem
5.8   Supply Chain Performance Optimization
5.9   A General (Non-Uniform) Circle Packing Problem
5.10   Further Application Perspectives

Concluding Notes
References