This class is intended as an introduction to the design and analysis of algorithms for numerical optimization. It is suitable for graduate students in the applied and natural sciences who want to develop an understanding of practical methods for optimization. If time permits, discussion will include some case studies involving real problems.
Specific topics will include the solution of nonlinear equations; Newton and quasi-Newton methods; optimality conditions; the Karush-Kuhn-Tucker conditions; linear, quadratic programming and nonlinear programming; convex programming; penalty- and barrier-function methods; interior-point methods; KKT systems and their numerical solution; augmented Lagrangian methods, sequential quadratic programming (SQP) methods.
Lecture notes are available to registered students from the Class Web-Site (see below). Many homework assignments will require the use of the interactive matrix package Matlab, although no prior knowledge of Matlab is assumed. Matlab enables the student to concentrate on the fundamental ideas of numerical optimization without becoming distracted by the rigors of mental arithmetic. (``It is unworthy of excellent men to lose hours like slaves in the labour of calculation.''---Leibniz.)
Optimization humor (pdf) (thanks to Michael Saunders).
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| Instructor: | Philip E. Gill | |
| Time: | MWF 1:00--1:50pm | |
| Class location: | AP&M Room 2402 | |
| Office Hours: | MW 11:00am--12:00pm, AP&M' Room 5872 (or by appointment) |