Optimization is central to any problem involving decision making, whether in engineering or in economics. The task of decision making entails choosing between various alternatives. This choice is governed by our desire to make the best decision. The measure of goodness of the alternatives is described by an objective function or performance index. Optimization theory and methods deal with selecting the best alternative in the sense of the given objective function. The area of optimization has received enormous attention in recent years, primarily because of the rapid progress in computer technology, including the development and availability of user-friendly software, high-speed and parallel processors, and artificial neural networks. A clear example of this phenomenon is the wide accessibility of optimization software tools such as the Optimization Toolbox of MATLAB and the many other commercial software packages. There are currently several excellent graduate textbooks on optimization theory and methods as well as undergraduate textbooks on the subject with an emphasis on engineering design. However, there is a need for an introductory textbook on optimization theory and methods at a senior undergraduate or beginning graduate level. The present text was written with this goal in mind. Some of the exercises require using MATLAB. The student edition of MATLAB is sufficient for all of the MATLAB exercises included in the text. The MATLAB source listings for the MATLAB exercises are also included in the solutions manual. The purpose of the book is to give the reader a working knowledge of optimization theory and methods. To accomplish this goal include many examples that illustrate the theory and algorithms discussed in the text. However, it is not our intention to provide a cookbook of the most recent numerical techniques for optimization; rather, our goal is to equip the reader with sufficient background for further study of advanced topics in optimization. The field of optimization is still a very active research area. In recent years, various new approaches to optimization have been proposed. In this text, it has been tried to reflect at least some of the flavor of recent activity in the area.
Dr. Eleftherios Garyfallidis holds the position of Associate Professor of Intelligent Systems Engineering (ISE) of Indiana University (IU) School of Informatics, Computing and Engineering. He is also the founder and scientific lead of Diffusion Imaging in Python (DIPY), currently the largest open source project in the development of diffusion MRI methods. Diffusion MRI is a unique non-invasive MRI technique that is used to study the structural connectivity of the brain. Dr. Garyfallidis holds a PhD from the University of Cambridge, UK, and worked as a Postdoctoral researcher with Professor Maxime Descoteaux at the Sherbrooke Connectivity Imaging Lab (SCIL) of the University of Sherbrooke, CA. Dr. Garyfallidis has performed research and development at nearly all levels of diffusion MRI analysis. Recently, he started focusing more on the problems of segmentation and registration of tractography. Some of his most known inventions are Quick Bundles and Streamline-based Linear Registration (SLR). Prof. Garyfallidis is leading this group for Neuroengineering at ISE specializing in the developing of new methods and intelligent algorithms for medical imaging and brain mapping with applications to research, clinic and industry.
Preface
Chapter 1. Introduction to Optimization
Chapter 2. Linear Programming (LP)
Chapter 3. Nonlinear Programming (NLP)
Chapter 4. Convex Optimization
Chapter 5. Unconstrained Optimization
Chapter 6. Constrained Optimization
Chapter 7. Integer and Combinatorial Optimization
Chapter 8. Multi-Objective Optimization
Chapter 9. Global Optimization
Bibliography
Index
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