Nonlinear Optimization with Engineering Applications
Bartholomew-Biggs, Michael.
creator
author.
SpringerLink (Online service)
text
xxu
2008
monographic
eng
access
XVI, 280 p. online resource.
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.
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.
by Michael Bartholomew-Biggs.
Mathematics
Mathematical optimization
Calculus of variations
Operations research
Management science
Mathematics
Optimization
Calculus of Variations and Optimal Control; Optimization
Operations Research, Management Science
QA402.5-402.6
519.6
Springer eBooks
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http://dx.doi.org/10.1007/978-0-387-78723-7
http://dx.doi.org/10.1007/978-0-387-78723-7
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