Nonlinear Optimization with Engineering Applications

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. *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.

Résumé
This 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.

Contenu

Introducing 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.