Nonlinear Optimization with Engineering Applications

1. Front Matter

   Pages 1-15

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2. Introducing Optimization

   • Michael Bartholomew–Biggs

   Pages 1-10

3. One-variable Optimization

   • Michael Bartholomew–Biggs

   Pages 1-22

4. Applications in n Variables

   • Michael Bartholomew–Biggs

   Pages 1-8

5. n-Variable Unconstrained Optimization

   • Michael Bartholomew–Biggs

   Pages 1-12

6. Direct Search Methods

   • Michael Bartholomew–Biggs

   Pages 1-10

7. Computing Derivatives

   • Michael Bartholomew–Biggs

   Pages 1-12

8. The Steepest Descent Method

   • Michael Bartholomew–Biggs

   Pages 1-8

9. Weak Line Searches and Convergence

   • Michael Bartholomew–Biggs

   Pages 1-8

10. Newton and Newton-like Methods

    • Michael Bartholomew–Biggs

    Pages 1-16

11. Quasi-Newton Methods

    • Michael Bartholomew–Biggs

    Pages 1-12

12. Conjugate Gradient Methods

    • Michael Bartholomew–Biggs

    Pages 1-12

13. ASummary of Unconstrained Methods

    • Michael Bartholomew–Biggs

    Pages 1-2

14. Optimization with Restrictions

    • Michael Bartholomew–Biggs

    Pages 1-8

15. Larger-Scale Problems

    • Michael Bartholomew–Biggs

    Pages 1-6

16. Global Unconstrained Optimization

    • Michael Bartholomew–Biggs

    Pages 1-8

17. Equality Constrained Optimization

    • Michael Bartholomew–Biggs

    Pages 1-14

18. Linear Equality Constraints

    • Michael Bartholomew–Biggs

    Pages 1-14

19. Penalty Function Methods

    • Michael Bartholomew–Biggs

    Pages 1-14

20. Sequential Quadratic Programming

    • Michael Bartholomew–Biggs

    Pages 1-14

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.

• algorithms
• global optimization
• linear optimization
• nonlinear optimization
• optimization
• quadratic programming
• scheduling

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)

• Dept. of Mathematics, University of Hertfordshire, Hatfield, United Kingdom

  Michael Bartholomew-Biggs

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