Practical Optimization: Algorithms and Engineering Applications

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Springer Science & Business Media, Dec 14, 2007 - Computers - 670 pages
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Practical Optimization: Algorithms and Engineering Applications provides a hands-on treatment of the subject of optimization. A comprehensive set of problems and exercises makes the book suitable for use in one or two semesters of a first-year graduate course or an advanced undergraduate course. Each half of the book contains a full semester’s worth of complimentary yet stand-alone material. The practical orientation of the topics chosen and a wealth of useful examples also make the book suitable as a reference work for practitioners in the field.

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

Key Features:

    • extensively class-tested
    • provides a complete teaching package with MATLAB exercises and online solutions to end-of-chapter problems

    • includes recent methods of emerging interest such as semidefinite programming and second-order cone programming
    • presents a unified treatment of unconstrained and constrained optimization
    • uses a practical treatment of optimization accessible to broad audience, from college students to scientists and industry professionals

    • provides a thorough appendix with background theory so non-experts can understand how applications are solved from point of view of optimization
 

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Contents

BASIC PRINCIPLES
27
GENERAL PROPERTIES OF ALGORITHMS 65
64
ONEDIMENSIONAL OPTIMIZATION
81
CONJUGATEDIRECTION METHODS
145
QUASINEWTON METHODS
175
FUNDAMENTALS OF CONSTRAINED OPTIMIZATION
265
THE SIMPLEX METHOD 321
320
LINEAR PROGRAMMING PART
369
SingularValue Decomposition
606
Orthogonal Projections
609
Householder Transformations and Givens Rotations
610
QR Decomposition
616
Cholesky Decomposition
619
Kronecker Product
621
Vector Spaces of Symmetric Matrices
623
Polygon Polyhedron Polytope and Convex Hull
626

QUADRATIC AND CONVEX PROGRAMMING
407
SEMIDEFINITE AND SECONDORDER CONE
449
GENERAL NONLINEAR OPTIMIZATION PROBLEMS
501
APPLICATIONS OF CONSTRAINED OPTIMIZATION 533
532
Appendices
591
Linear Independence and Basis of a Span
592
Range Null Space and Rank
593
ShermanMorrison Formula
595
Eigenvalues and Eigenvectors
596
A6 Symmetric Matrices
598
Trace
602
References
627
B Basics of Digital Filters 629
628
TimeDomain Response
631
Stability Property
632
Transfer Function
633
TimeDomain Response Using the Z Transform
635
Frequency Amplitude and Phase Responses
636
Design
639
Reference
644
Index
645
Copyright

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About the author (2007)

Andreas Antoniou received the Ph.D. degree in Electrical Engineering from the University of London, UK, in 1966 and is a Fellow of the IET and IEEE. He served as the founding Chair of the Department of Electrical and Computer Engineering at the University of Victoria, B.C., Canada, and is now Professor Emeritus in the same department. He is the author of Digital Filters: Analysis, Design, and Applications (McGraw-Hill, 1993) and Digital Signal Processing: Signals, Systems, and Filters (McGraw-Hill, 2005). He served as Associate Editor/Editor of IEEE Transactions on Circuits and Systems from June 1983 to May 1987, as a Distinguished Lecturer of the IEEE Signal Processing Society in 2003, as General Chair of the 2004 International Symposium on Circuits and Systems, and is currently serving as a Distinguished Lecturer of the IEEE Circuits and Systems Society. He received the Ambrose Fleming Premium for 1964 from the IEEE (best paper award), the CAS Golden Jubilee Medal from the IEEE Circuits and Systems Society, the B.C. Science Council Chairman’s Award for Career Achievement for 2000, theDoctorHonoris Causa degree from the Metsovio National Technical University of Athens, Greece, in 2002, and the IEEE Circuits and Systems Society 2005 Technical Achievement Award.

Wu-Sheng Lu received the B.S. degree in Mathematics from Fudan University, Shanghai, China, in 1964, the M.E. degree in Automation from the East China Normal University, Shanghai, in 1981, the M.S. degree in Electrical Engineering and the Ph.D. degree in Control Science from the University of Minnesota, Minneapolis, in 1983 and 1984, respectively. He was a post-doctoral fellow at the University of Victoria, Victoria, BC, Canada, in 1985 and Visiting Assistant Professor with the University of Minnesota in 1986. Since 1987, he has been with the University of Victoria where he is Professor. His current teaching and research interests are in the general areas of digital signal processing and application of optimization methods. He is the co-author with A. Antoniou of Two-Dimensional Digital Filters (Marcel Dekker, 1992). He served as an Associate Editor of the Canadian Journal of Electrical and Computer Engineering in 1989, and Editor of the same journal from 1990 to 1992. He served as an Associate Editor for the IEEE Transactions on Circuits and Systems, Part II, from 1993 to 1995 and for Part I of the same journal from 1999 to 2001 and from 2004 to 2005. Presently he is serving as Associate Editor for the International Journal of Multidimensional Systems and Signal Processing. He is a Fellow of the Engineering Institute of Canada and the Institute of Electrical and Electronics Engineers.