# Practical Optimization: Algorithms and Engineering Applications

Springer Science & Business Media, Dec 14, 2007 - Computers - 670 pages

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