【2018新书】优化基础（Fundamentals of Optimization）

【2018新书】优化基础（Fundamentals of Optimization  Methods, Minimum Principles, and Applications for Making Things Better）
Mark french Fundamentals of optimization Methods, Minimum Principles and Applications for Making Things Better Springer Mark french School of Engineering Technology Purdue university West Lafayette, IN, USA ISBN9783319761916 ISBN9783319761923( ebook) https://doi.org/10.1007/9783319761923 Library of Congress Control Number: 2018935277 C Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Printed on acidfree paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer nature The registered company address is: Gewerbestrasse 11, 6330 Cham, switzerland Foreword I have had the great pleasure in getting to know Mark Frenchs dedication and innovative ways of teaching engineering principles over the last few years. Mark is truly an exceptional teacher and this is reflected in his latest work: Fundamentals of Optimization: Methods, Minimum Principles, and Applications for Making Things Better. The best textbook authors for education tend to be those that have a strong desire to simplify and present difficult topics in such a way as to carefully lead the student along a learning journey that builds self confidence in the subject. Being an author of numerous textbooks myself, I know that dedicated teachers make great textbook authors and mark's dedication is reflected in his book This book is an introductory treatise on the topic of optimization in engineering design. The point of this book is to provide a reference for students and professionals who need a clear introduction to optimization, with actionable information and examples that show how the calculations work. this is basically the book mark French needed when he learned to use optimization as a civilian aerospace engineer with the us air force There are a number of mathematically rigorous optimization books in print and some are very good, but they are generally geared towards researchers and advanced graduate students. They tend toward abstract and theoretical presentations often going so far as to introduce subjects using a mathematically formal statementproof structure. While this is quite appropriate for the research community, it is the wrong approach for students who need to learn how to improve processes and products The main features of the book that make it useful for teaching and learning include the A focus on meaningful, less abstract problems Sample calculations including intermediate results ple cal Preference for accessible. robust methods Examples showing implementation in MATLAB Graphical results whenever possible orewor Historical and industrial examples to give context to the development of optimization Each chapter steps the reader through example problems, which include text explaining the process, the calculations, and the graphic representation of the results This stepbystep learning process is an ideal teaching methodology that leads the learner through the concept being presented in a format that is easy to follow and understand. The use of realworld examples is especially compelling as it has the potential to draw the learner into the problem. As we know a selfmotivated learner gaged and interested in DIc Overall, Mark French has written a book that is very compelling in its approach, and his writing style and use of examples are some of the best i have seen in mathematics textbooks Mark is an outstanding classroom teacher and that is eflected in this book Purdue University, West Lafayette Gary bertoline IN. USA Preface This is an optimization book for people who need to solve problems. It is written for those who know very little maybe nothing about optimization, but need to understand basic methods well enough to apply them to practical problems. A survey of available books on optimization finds a number of very good ones, but often ones written using highlevel mathematics and sometimes even written in a statement proof format. Clearly, these books are valuable for people wishing to work at a high level of technical sophistication, but they are sometimes opaque to people needing, rather, an accessible introduction. I think there needs to be a book that brings a reader from a point of knowing next to nothing to a point of knowing the big ideas, the necessary vocabulary, a group of simple and robust methods, and, above all, a sense of how optimization can be used This book has resulted from years of teaching optimization to both engineering and engineering technology students and from years spent applying optimization methods to problems of practical interest. Its content has been tested on many classrooms full of inquisitive students, and only the lessons they think were suc cessful appear here The number of methods presented here is small; I have selected a few simple robust methods to describe in detail so that readers can develop a useful mental framework for understanding how information is processed by optimization soft ware. While more sophisticated methods are certainly more efficient, they dont look that different to the user Thus, this book sticks to the simple, robust, and access sible methods I have used two calculation tools. Mathcad and matlab. matlab is at this writing, probably the standard tool for general technical calculation, at least in the United States and much of Europe. The more sophisticated plots and more extensive calculations in this book were generally done using matlab. However MatLaB is a programming language that looks familiar to anyone who ever learned FOR TRAN. While quite powerful, MATLAB code, especially efficient, vectorized code can be very difficult to read a real problem for a book like this Preface Mathcad is a very different animal, designed to make smaller calculations simply and with little need for formal programming. It is essentially a math scratchpad that is easy to use and easy to read. i chose to illustrate the details of specific calculations using Mathcad because even readers who are new to Mathcad can probably read the sample files, even if they could not write them. The Mathcad files in this book were made using Mathcad V15. The name Mathcad is not, in my opinion, a very good one, though I very much like the software. It has nothing to do with CAD or graphics software Finally, I hope this book will serve the needs of analysts for whom the result is more important than the algorithm Those who wish eventually to study the behavior of algorithms and to perhaps even develop better methods may, I hope, find this volume a useful start before moving on to more advanced texts West Lafayette in. uSa Mark french Acknowledgments Every author knows that a book is the result of many contributions my students continue to make sure that i know what I,m talking about and remind me when my explanations aren t clear enoug When I was a new engineer at what was then called the air Forces flight Dynamics Lab, Ray Kolonay, Bob Canfield, and V B 'Van'Venkayya collectively helped teach me how the ideas of optimization worked and how to apply them Working on their astros project was a time of great learning for me and i hope i was of some value to them Over the years, I have been fortunate to participate in many different projects and work with some outstanding colleagues. From them, I learned about how the engineering concepts I learned in school are applied. These people are too numerous to name here and i hope they will forgive the omission. Perhaps it is enough to simply acknowledge my debt to them Kay solomon continues to be the person to whom I can go for help with line editing and for help in turning clumsy phrasing into something more readable. Her literary fabulosity glows undiminished. Everyone should, as i do, know someone who likes to read the dictionary I am fortunate to work in a place where I can do things like write optimization books. I'm not a conventional professor and would probably be an interference fit in most academic environments. It is my great good fortune to have found a place where i can thrive My beloved wife, Amy, has now suffered through three books and, inexplicably retains her patience and good humor. Finally, I wish to thank Ken Burbank for being the best boss I've ever had. This book is dedicated to him Contents 1 Optimization: The Big Idea gn Spa 1. 2 What Is Optimum? 8 Refe 2 Getting Started in Optimization: Problems of a Single variable 15 2.1 The Lifeguard probl 15 2.2 Maximum Range of a Projectile with Aerodynamics 18 2. 3 Maximum Electrical Power delivered to a load 21 2.4 Shortest Time Path for a Toy car 2 2.5 Weight on a SnapThrough Spring 27 2.6 Solution methods..,,.,,,.,,,,,,,,,,,,. 29 2.6.1 Analytical Solution 30 2.6.2 Monte Carlo method 32 2.6.3 Binary Search 32 2.6.4 Quadratic Approximation Method 36 2.6.5 Hybrid Methods 39 2.7 Finding Roots Using Minimization 2.8 Optimizing a Process: Ocean Shipping routes 43 2.9 MATLAB Examples............ 51 References 54 3 Minimum Principles: Optimization in the Fabric of the Universe 3.1 Evolution 55 3.2 Minimum Energy Structures 58 3.3 Optics: Fermats Principle and Snell,s Laws 66 3.4 General Relativity 69 R eferences 70
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