This text is a complete overview of optimization from basic preliminaries (definitions of convex functions, what optimization is, etc.) on to application of specific approaches, such as the interior point algorithm and the active set method. The table of contents and text itself reference page numbers and content not printed in the book. This material, which covers rudimentary preliminaries, such as notation, linear algebra basics, and more, is available from the publisher’s site. I had no problem downloading the material in PDF format, along with hundreds of pages of prepared teaching material. Exercise solutions can only be downloaded by instructors and the text provides no exercise solutions.
The gist of this book is to patiently and completely provide a foundation for developing techniques to formulate numerical problems so that they can be solved by existing software. The actual use of such software is not articulated in detail. The Matlab Optimization Toolbox is in the author's mind here, but do not expect code samples or syntax guidelines. The focus is on introducing a taxonomy of numerical problems and techniques for solving them. Engineering case studies (circuit design, storage of sparse matrices, least-cost production, etc.) are used to illustrate in detail the formulation process.
Five general problem classes are considered: linear systems of equations, non-linear systems of equations, unconstrained optimization, equality constrained optimization, and inequality constrained optimization. In order to supply depth, the author forgoes more exotic subjects in optimization that are afforded only a cursory overview in other texts on the topic. Problem features such as monotonicity, convexity, symmetry, and sparsity are given focus.
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.