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Fundamentals of Optimization

Methods, Minimum Principles, and Applications for Making Things Better

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Publisher:

Springer

Pages: 249
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Recommend to library

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Hardcover - 9783319761916

18 May 2018

$84.99

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This textbook is for readers new or returning to the practice of optimization whose interest in the subject may relate to a wide range of products and processes. Rooted in the idea of “minimum principles,” the book...

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This textbook is for readers new or returning to the practice of optimization whose interest in the subject may relate to a wide range of products and processes. Rooted in the idea of “minimum principles,” the book introduces the reader to the analytical tools needed to apply optimization practices to an array of single- and multi-variable problems. While comprehensive and rigorous, the treatment requires no more than a basic understanding of technical math and how to display mathematical results visually. It presents a group of simple, robust methods and illustrates their use in clearly-defined examples. Distinct from the majority of optimization books on the market intended for a mathematically sophisticated audience who might want to develop their own new methods of optimization or do research in the field, this volume fills the void in instructional material for those who need to understand the basic ideas. 

The text emerged from a set of applications-driven lecture notes used in optimization courses the author has taught for over 25 years. The book is class-tested and refined based on student feedback, devoid of unnecessary abstraction, and ideal for students and practitioners from across the spectrum of engineering disciplines. It provides context through practical examples and sections describing commercial application of optimization ideas, such as how containerized freight and changing sea routes have been used to continually reduce the cost of moving freight across oceans. It also features 2D and 3D plots and an appendix illustrating the most widely used MATLAB optimization functions. 

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  • Facilitates a solid grasp of the core concepts in optimization for students with no more than a background in basic technical math (derivatives);
  • Maximizes reader understanding by focusing on a select group of simple, robust methods;
  • Reinforces concepts with many numerical examples done in MathCAD clearly showing the intermediate calculations along with final results;
  • Provides context through practical examples, including discussions of how optimization is used in commercial applications;
  • Illustrates results graphically.

Optimization: The Big Ideas
Getting Started in Optimization: Problems with a Single Variable
Minimum Principles - Optimization in the Fabric of the Universe
Problems with More Than One Variable
Constraints – Placing Limits on the Solution
General Conditions for Solving Optimization Problem – Karush Kuhn Tucker Conditions
Discrete Variables
Aerospace Applications
Structural Optimization
Multi-objective Optimization
Appendix A - Calculus Refresher
Appendix B - Test Functions
Appendix C - Solving Optimization Problems using MATLAB.-

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Dr. Mark French is Professor of Engineering at Purdue University. He began his career as a civilian aerospace engineer in the Analysis and Optimization Branch of what was then the Flight Dynamics Lab at Wright-Patterson Air Force Base. Over the course of 10 years there, he worked on a range of problems in optimization, aeroelasticity and photomechanics. He then moved to the automotive industry, where he spent nine years as an engineer and a lab manager, specializing in noise and vibration problems. While there, he also began to do informal work for the guitar industry. He came to Purdue University in 2004, where he is now a professor in the School of Engineering Technology. He...

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Dr. Mark French is Professor of Engineering at Purdue University. He began his career as a civilian aerospace engineer in the Analysis and Optimization Branch of what was then the Flight Dynamics Lab at Wright-Patterson Air Force Base. Over the course of 10 years there, he worked on a range of problems in optimization, aeroelasticity and photomechanics. He then moved to the automotive industry, where he spent nine years as an engineer and a lab manager, specializing in noise and vibration problems. While there, he also began to do informal work for the guitar industry. He came to Purdue University in 2004, where he is now a professor in the School of Engineering Technology. He has authored numerous papers as well as two books on the technical aspects of guitar design.

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