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OverviewThis book, like its companion volume Nonlinear Optimization with Financial Applications, is an outgrowth of undergraduate and po- graduate courses given at the University of Hertfordshire and the University of Bergamo. It deals with the theory behind numerical methods for nonlinear optimization and their application to a range of problems in science and engineering. The book is intended for ?nal year undergraduate students in mathematics (or other subjects with a high mathematical or computational content) and exercises are provided at the end of most sections. The material should also be useful for postg- duate students and other researchers and practitioners who may be c- cerned with the development or use of optimization algorithms. It is assumed that readers have an understanding of the algebra of matrices and vectors and of the Taylor and mean value theorems in several va- ables. Prior experience of using computational techniques for solving systems of linear equations is also desirable, as is familiarity with the behaviour of iterative algorithms such as Newton’s methodfor nonlinear equations in one variable. Most of the currently popular methods for continuous nonlinear optimization are described and given (at least) an intuitive justi?cation. Relevant convergence results are also outlined and we provide proofs of these when it seems instructive to do so. This theoretical material is complemented by numerical illustrations which give a ?avour of how the methods perform in practice. Full Product DetailsAuthor: Michael Bartholomew-BiggsPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of hardcover 1st ed. 2008 Volume: 19 Dimensions: Width: 15.50cm , Height: 1.50cm , Length: 23.50cm Weight: 0.456kg ISBN: 9781441946218ISBN 10: 1441946217 Pages: 280 Publication Date: 08 December 2010 Audience: Professional and scholarly , Professional & Vocational , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroducing Optimization.- One-variable Optimization.- Applications in n Variables.- n-Variable Unconstrained Optimization.- Direct Search Methods.- Computing Derivatives.- The Steepest Descent Method.- Weak Line Searches and Convergence.- Newton and Newton-like Methods.- Quasi-Newton Methods.- Conjugate Gradient Methods.- ASummary of Unconstrained Methods.- Optimization with Restrictions.- Larger-Scale Problems.- Global Unconstrained Optimization.- Equality Constrained Optimization.- Linear Equality Constraints.- Penalty Function Methods.- Sequential Quadratic Programming.- Inequality Constrained Optimization.- Extending Equality Constraint Methods.- Barrier Function Methods.- Interior Point Methods.- A Summary of Constrained Methods.- The OPTIMA Software.ReviewsFrom the reviews: This book gives on 280 pages a broad overview of nonlinear optimization. ... The presented optimization approaches are compared with each other by means of several examples with up to 200 variables. ... the introduction of the different techniques is written in a very comprehensible way. ... each section contains exercises to verify and deepen the understanding of the material. (Andrea Walther, Zentralblatt MATH, Vol. 1167, 2009) From the reviews: This book gives on 280 pages a broad overview of nonlinear optimization. ! The presented optimization approaches are compared with each other by means of several examples with up to 200 variables. ! the introduction of the different techniques is written in a very comprehensible way. ! each section contains exercises to verify and deepen the understanding of the material. (Andrea Walther, Zentralblatt MATH, Vol. 1167, 2009) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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