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. For example, we include a discussion of genetic algorithms, a topic of increasing importance in the study of complex adaptive systems. There has also been a recent surge of applications of optimization methods to a variety of new problems. A prime example of this is the use of descent algorithms for the training of feed forward neural networks.
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