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Author Bartholomew-Biggs, Michael C.

Title Nonlinear optimization with engineering applications / by Michael Bartholomew-Biggs
Published New York, NY : Springer, [2008]
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Description 1 online resource (xvi, 280 pages) : illustrations
Series Springer optimization and its applications ; v. 19
Springer optimization and its applications ; v. 19
Contents Preface -- 1. Introduction to engineering optimization problems -- 2. Some engineering problems in one variable -- 3. Numerical optimization in one variable -- 4. Route-planning and other problems in several variables -- 5. Gradients, Hessians and automatic differentiation -- 6. Optimality conditions for n variable unconstrained problems -- 7. Steepest descent method -- 8. Newton method -- 9. Quasi-Newton methods -- 10. Conjugate gradient methods -- 11. Problem transformations to handle constraints -- 12. Maintenance scheduling -- a case study -- 13. Data fitting and identification -- 14. The Gauss-Newton method with examples -- 15. Power system scheduling and engineering problems involving constraints -- 16. Optimality conditions for equality constrained problems -- 17. Quadratic programming and reduced gradients with examples -- 18. Penalty function methods and examples -- 19. Sequential QP methods -- 20. Trajectory optimization- a case study -- 21. Wing design and other problems involving inequality constraints -- 22. Optimality conditions for inequality constrained problems -- 23. Extending equality methods for inequalities -- 24. Barrier methods -- 25. Interior point methods -- 26. Further trajectory optimization problems -- 27. Global optimization -- 28. Route-planning -- a case study -- Index
Summary 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
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Mathematical optimization.
Nonlinear theories.
Engineering mathematics.
Form Electronic book
ISBN 0387787232 (electronic bk.)
9780387787237 (electronic bk.)