Über die Autorin bzw. den Autor

P. Venkataraman, PhD, is an associate professor in the Mechanical Engineering Department, Rochester Institute of Technology, Rochester, New York.

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Technology/Engineering/Mechanical

Provides all the tools needed to begin solving optimization problems using MATLAB®

The Second Edition of Applied Optimization with MATLAB® Programming enables readers to harness all the features of MATLAB® to solve optimization problems using a variety of linear and nonlinear design optimization techniques. By breaking down complex mathematical concepts into simple ideas and offering plenty of easy-to-follow examples, this text is an ideal introduction to the field. Examples come from all engineering disciplines as well as science, economics, operations research, and mathematics, helping readers understand how to apply optimization techniques to solve actual problems.

This Second Edition has been thoroughly revised, incorporating current optimization techniques as well as the improved MATLAB® tools. Two important new features of the text are:

• Introduction to the scan and zoom method, providing a simple, effective technique that works for unconstrained, constrained, and global optimization problems

• New chapter, Hybrid Mathematics: An Application, using examples to illustrate how optimization can develop analytical or explicit solutions to differential systems and data-fitting problems

Each chapter ends with a set of problems that give readers an opportunity to put their new skills into practice. Almost all of the numerical techniques covered in the text are supported by MATLAB® code, which readers can download on the text's companion Web site www.wiley.com/go/venkat2e and use to begin solving problems on their own.

This text is recommended for upper-level undergraduate and graduate students in all areas of engineering as well as other disciplines that use optimization techniques to solve design problems.

Aus dem Klappentext

Technology/Engineering/Mechanical

Provides all the tools needed to begin solving optimization problems using MATLAB®

The Second Edition of Applied Optimization with MATLAB® Programming enables readers to harness all the features of MATLAB® to solve optimization problems using a variety of linear and nonlinear design optimization techniques. By breaking down complex mathematical concepts into simple ideas and offering plenty of easy-to-follow examples, this text is an ideal introduction to the field. Examples come from all engineering disciplines as well as science, economics, operations research, and mathematics, helping readers understand how to apply optimization techniques to solve actual problems.

This Second Edition has been thoroughly revised, incorporating current optimization techniques as well as the improved MATLAB® tools. Two important new features of the text are:

• Introduction to the scan and zoom method, providing a simple, effective technique that works for unconstrained, constrained, and global optimization problems

• New chapter, Hybrid Mathematics: An Application, using examples to illustrate how optimization can develop analytical or explicit solutions to differential systems and data-fitting problems

Each chapter ends with a set of problems that give readers an opportunity to put their new skills into practice. Almost all of the numerical techniques covered in the text are supported by MATLAB® code, which readers can download on the text's companion Web site www.wiley.com/go/venkat2e and use to begin solving problems on their own.

This text is recommended for upper-level undergraduate and graduate students in all areas of engineering as well as other disciplines that use optimization techniques to solve design problems.

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Applied Optimazation with MATLAB Programming

John Wiley & Sons

Chapter One

Optimization is, in essence, a search for the best objective when operating within a set of constraints. For example you want the lightest car that can at least deliver standard performance and possess good safety features while being powered a hybrid engine. Maybe you want to generate maximum shareholder return on investment while meeting the 10 percent sales growth and holding inventory at the minimum. Sometimes you want to minimize commuting time by choosing alternate routes during peak traffic periods. You can come up with several examples of this kind from everyday experience. What you have done is loosely define an optimization problem that needs a solution. The procedure by which you will establish a solution to the above examples uses optimization techniques. A second read through these sentences will suggest you are really talking about designs that are qualified by the words lightest, maximum, minimize. All of these, and many others like it can be described by the word optimum. In addition, these designs must be within a certain envelope or satisfy certain conditions or must be limited, if they are to be acceptable. These are the constraints on the design. With this basic definition you can identify problems of design optimization. Most of the book is about formally expressing these kinds of problems and looking at several techniques that can be employed to establish the solution.

Optimization is an essential part of design activity in all major disciplines. These disciplines are not restricted to engineering. In product development, competition demands producing economically relevant products with embedded quality. Today, globalization demands that additional dimensions such as location, language, and expertise must also merit consideration as new constraints in the development process. Improved production and design tools coupled with inexpensive computational resources have made optimization an important part of the process. Even in the absence of a tangible product, optimization ideas provide the ability to define and explore problems while focusing on solutions that subscribe to some measure of usefulness. Generally, the use of the word optimization implies the best result under the circumstances. This includes the particular set of constraints on the development resources, current knowledge, market conditions, and so on. The ability to make the best choice is a perpetual desire among us all. The techniques that are used in optimization are also used for obtaining solutions to nonlinear problems in many disciplines-so the subject has an attraction to a wider audience from many fields.

In this book, optimization is often associated with design, be it a product, service or a strategy. Aerospace design was among the earliest disciplines to embrace optimization in a significant way driven by a natural need to lower the tremendous cost associated with carrying unnecessary weight in aerospace vehicles. Minimum mass structures are the norm. It forms part of the psyche of every aerospace designer. Just recently, Boeing introduced the Dreamliner to the world. The aircraft uses more than 50% plastic in its structure, replacing metals, without compromising on safety. Today, an emerging discipline is multidisciplinary optimization (MDO) of greater significance to aerospace designers, where structural design and aerodynamics are combined to produce an optimal vehicle shape. A good example is the Boeing blended wing-body design. Saving on fuel through trajectory design was another problem that suggested itself. Very soon, the entire engineering community could recognize the need to define solutions based on merit.

Recognizing the desire for optimization and actually implementing it has taken some time to mature. In the past, optimization was usually attempted only in those situations where there were significant penalties for generic designs. The application of optimization demanded large computational resources. In the nascent years of digital computation, these were available only to large national laboratories and programs. These resources were necessary to handle the nonlinear problems that are associated with engineering optimization. As a result of these constraints most of the everyday products were designed without regard to optimization.

Today, it is inconceivable that current replacement products, such as the car, the house, the desk, the pencil, and so on, are not designed optimally in some sense or another. The most obvious contemporary example of the use of optimization manifests in the same streamlined bubblelike look in all cars from all manufacturers. Minimizing drag coefficient, particularly through software, improves fuel consumption. This is an easier option for meeting fuel consumption standards without requiring a change in the engine performance, which has proved very stubborn.

Today, you would definitely explore procedures to optimize your investments by tailoring your portfolio. You would optimize your business travel time by appropriately choosing your destinations. You can optimize your commuting time by choosing your time and route. You can optimize your necessary expenditure for living by choosing your day and store for shopping. You can buy software that will optimize your connection to the Internet. You can have affordable access to resources that will allow you to perform all these various optimizations. Seeing the variety of problems that need to generate optimum solutions, the study of optimization is actually more of a tool that can be applied to a variety of disciplines. If so, all of the optimization problems from many disciplines should be described in a common way.

The partnership between design and optimization activity is still more often found in engineering. This book recognizes that connection. Much of the problems used for illustrations and practice are from engineering, primarily mechanical, civil, and aerospace design. Nevertheless, the study of optimization, particularly applied optimization, is not an exclusive property of any specific discipline. It involves the discovery and design of solutions through appropriate techniques associated with the formulation of the problem in a specific manner. This can be done for example, in economics, chemistry, and business management. A Google search on "optimization of", at the time of this writing, resulted in 128 million hits, the first six of them related to optimization in digital circuits, trading system, immunomagnetic separation, object-oriented programming, risk measures, and chemical process.

1.1 OPTIMIZATION FUNDAMENTALS

Optimization was described as the process of search for the solution that is more useful than several others. Qualitatively, this assertion implicitly recognizes the necessity of choosing among alternatives. This book deals with optimization in a quantitative way. This means that an outcome of applying optimization techniques to the problem, design, or service must yield numbers that will define our solution-in other words, numbers or values that will characterize the particular design or service. Quantitative description of the solution requires a quantitative...