Applied Optimization: Formulation and Algorithms for Engineering Systems
The starting point in the formulation of any numerical problem is to take an intuitive idea about the problem in question and to translate it into precise mathematical language. This book provides step-by-step descriptions of how to formulate numerical problems so that they can be solved by existing software. It examines various types of numerical problems and develops techniques for solving them. A number of engineering case studies are used to illustrate in detail the formulation process. The case studies motivate the development of efficient algorithms that involve, in some cases, transformation of the problem from its initial formulation into a more tractable form. Five general problem classes are considered: linear systems of equations, non-linear systems of equations, unconstrained optimization, equality constrained optimization, and inequality constrained optimization. The book contains many worked examples and homework exercises and is suitable for students of engineering or operations research taking courses in optimization. For appendices, teaching materials, and Instructor's solutions for homework exercises in the book, please follow the 'resources and solutions' link on this page.
Uses case studies to illustrate formulation of problems, emphasizing problem features such as monotonicity, convexity, symmetry, and sparsity ¿ Large number of homework exercises and worked examples: solution set available for instructors. ¿ Two appendices, of mathematical preliminaries and of proofs, available for downloading
Table of Contents
1. Introduction; 2. Problems, algorithms, and solutions; 3. Transformation of problems; Part I. Linear Simultaneous Equations: 4. Case studies; 5. Algorithms; Part II. Non-linear Simultaneous Equations: 6. Case studies; 7. Algorithms; 8. Solution of the case studies; Part III. Unconstrained Optimization: 9. Case studies; 10. Algorithms; 11. Solution of the case studies; Part IV. Equality Constrained Optimization: 12. Case studies; 13. Algorithms for linear constraints; 14. Algorithms for non-linear constraints; Part V. Inequality Constrained Optimization: 15. Case studies; 16. Algorithms for non-negativity constraints; 17. Algorithms for linear constraints; 18. Solution of the case studies; 19. Algorithms for non-linear constraints; 20. Solution of the case studies; References; Index.