Andreas Antoniou - Practical Optimization: Algorithms and Engineering Applications

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Optimization methods and algorithms continue to evolve at a tremendous rate and are providing solutions to many problems that could not be solved before in economics, finance, geophysics, molecular modeling, computational systems biology, operations research, and all branches of engineering (see the following link for details: https://en.wikipedia.org/wiki/Mathematical_optimization#Molecular_modeling ).

The growing demand for optimization methods and algorithms has been addressed in the second edition by updating some material, adding more examples, and introducing some recent innovations, techniques, and methodologies. The emphasis continues to be on practical methods and efficient algorithms that work.

Chapters , a new section has been added that deals with the application of the conjugate-gradient method for the solution of linear systems of equations.

In Chap. , some state-of-the art applications of unconstrained optimization to machine learning and source localization are added. The first application is in the area of character recognition and it is a method for classifying handwritten digits using a regression technique known as softmax. The method is based on an accelerated gradient descent algorithm. The second application is in the area of communications and it deals of the problem formulation and solution methods for identifying the location of a radiating source given the distances between the source and several sensors.

The contents of Chaps. of the first edition.

Chapter . It also describes several algorithms for the solution of general convex problems and includes a detailed exposition of the so-called alternating direction method of multipliers (ADMM).

Chapter is a new chapter that focuses on sequential convex programming, sequential quadratic programming, and convex-concave procedures for general nonconvex problems. It also includes a section on heuristic ADMM techniques for nonconvex problems.

In Chap. , we have added some new state-of-the art applications of constrained optimization for the design of Finite-Duration Impulse Response (FIR) and Infinite-Duration Impulse Response (IIR) digital filters, also known as nonrecursive and recursive filters, respectively, using second-order cone programming. Digital filters that would satisfy multiple specifications such as maximum passband gain, minimum stopband gain, maximum transition-band gain, and maximum pole radius, can be designed with these methods.

The contents of Appendices A and B are largely unchanged except for some editorial changes.

Many of our past students at the University of Victoria have helped a great deal in improving the first edition and some of them, namely, Drs. M. L. R. de Campos, Sunder Kidambi, Rajeev C. Nongpiur, Ana Maria Sevcenco, and Ioana Sevcenco have provided meaningful help in the evolution of the second edition as well. We would also like to thank Drs. Z. Dong, T. Hinamoto, Y. Q. Hu, and W. Xu for useful discussions on optimization theory and its applications, Catherine Chang for typesetting the first draft of the second edition, and to Lynne Barrett for checking the entire second edition for typographical errors.

The rapid advancements in the efficiency of digital computers and the evolution of reliable software for numerical computation during the past three decades have led to an astonishing growth in the theory, methods, and algorithms of numerical optimization. This body of knowledge has, in turn, motivated widespread applications of optimization methods in many disciplines, e.g., engineering, business, and science, and led to problem solutions that were considered intractable not too long ago.

Although excellent books are available that treat the subject of optimization with great mathematical rigor and precision, there appears to be a need for a book that provides a practical treatment of the subject aimed at a broader audience ranging from college students to scientists and industry professionals. This book has been written to address this need. It treats unconstrained and constrained optimization in a unified manner and places special attention on the algorithmic aspects of optimization to enable readers to apply the various algorithms and methods to specific problems of interest. To facilitate this process, the book provides many solved examples that illustrate the principles involved, and includes, in addition, two chapters that deal exclusively with applications of unconstrained and constrained optimization methods to problems in the areas of pattern recognition, control systems, robotics, communication systems, and the design of digital filters. For each application, enough background information is provided to promote the understanding of the optimization algorithms used to obtain the desired solutions.