This outline is a tentative guide.
The topic of Fall, 1998 is Verified Global Optimization. The course format will be a combination of student presentations and lecture / discussion. Specific topics are represented in the books Rigorous Global Search: Continuous Problems and Numerica: A Modelling Language for Scientific Computation. Emphasis will be on effective branch and bound structures, including when interval Newton methods are used, bisection strategies, van Hentenryck's technique and other constraint satisfaction techniques, and epsilon inflation / set complementation. Students will work with the GlobSol software package and with Numerica.
Progress will be posted here.
| References | Description | |
| 1. | Empirical Evaluation of Innovations in Interval Branch and Bound Algorithms for Nonlinear Algebraic Systems, and also Chapter 4.1 of Rigorous Global Search: Continuous Problems | A review of branch and bound algorithms for nonlinear algebraic systems of equations. The instructor will present the overall algorithm structure. |
| 2. | http://www.mscs.mu.edu/~globsol/, and, in particular, http://www.mscs.mu.edu/~globsol/User_Guide/ | An introduction to GlobSol, with emphasis on how to use the package for nonlinear systems of equations. |
| 3. | Chapter 3 of Gill / Murray / Wright | Optimality conditions for nonlinearly constrained optimization; Lagrange multipliers. |
| 4. | The preprint "An Iterative Method for Finding Approximate Feasible Points" | Locating points on the feasible set of general (simultaneous inequality and equality) constraints. |
| 5. | Chapter 5 of Rigorous Global Search: Continuous Problems, and the GlobSol software itself. | Techniques for solving constrained problems in GlobSol. |
| 6. | Selected portions of Numerica: A Modelling Language for Scientific Computation. | Logic programming constraint propagation techniques; one-dimensional region elimination using constraints. |
| 7. | Portions of Gill, Murray, and Wright, Practical Optimization, and selected library and internet resources. | Traditional techniques for finding approximate local optimizers in nonlinearly constrained nonlinear optimization problems. |
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