This textbook examines a broad range of problems in science and engineering, describing key numerical methods applied to real life. The case studies presented are in such areas as data fitting, vehicle route planning and optimal control, scheduling and resource allocation, sensitivity calculations and worst-case analysis. Among the main topics covered: * one-variable optimization — optimality conditions, direct search and gradient
* unconstrained optimization in n variables — solution methods including Nelder and Mead simplex, steepest descent, Newton, Gauss–Newton, and quasi-Newton techniques, trust regions and conjugate gradients
* constrained optimization in n variables — solution methods including reduced-gradients, penalty and barrier methods, sequential quadratic programming, and interior point techniques
* an introduction to global optimization * an introduction to automatic differentiation Chapters are self-contained with exercises provided at the end of most sections. <EM>Nonlinear Optimization with Engineering Applications is ideal for self-study and classroom use in engineering courses at the senior undergraduate or graduate level. The book will also appeal to postdocs and advanced researchers interested in the development and use of optimization algorithms. Also by the author: Nonlinear Optimization with Financial Applications, ISBN: 978-1-4020-8110-1, (c)2005, Springer.
NONLINEAR OPTIMIZATION WITH ENGINEERING APPLICATIONS
Springer Optimization and Its Applications VOLUME 19 Managing Editor Panos M. Pardalos (University of Florida) Editor—Combinatorial Optimization Ding-Zhu Du (University of Texas at Dallas) Advisory Board J. Birge (University of Chicago) C.A. Floudas (Princeton University) F. Giannessi (University of Pisa) H.D. Sherali (Virginia Polytechnic and State University) T. Terlaky (McMaster University) Y. Ye (Stanford University)
Aims and Scope Optimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics and other sciences. The Springer Series in Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multiobjective programming, description of software packages, approximation techniques and heuristic approaches.
NONLINEAR OPTIMIZATION WITH ENGINEERING APPLICATIONS
By MICHAEL BARTHOLOMEW-BIGGS University of Hertfordshire, UK
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Michael Bartholomew-Biggs Department of Mathematics University of Hertfordshire Hatfield AL10 9AB United Kingdom
[email protected]
ISBN: 978-0-387-78722-0 DOI: 10.1007/978-0-387-78723-7
e-ISBN: 978-0-387-78723-7
Library of Congress Control Number: 2008923327 Mathematics Subject Classification (2000): 90-01, 90-08, 65K05 c 2008 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied