Numerical Methods for Nonlinear Optimization
Computer Science 6676, Spring 1999
January 11, 1999
This course will discuss numerical methods for solving three important nonlinear algebra problems: solving systems of nonlinear equations, finding the minimum or maximum of a nonlinear function of multiple variables (unconstrained optimization), and nonlinear least squares. We will cover both the mathematical derivation of the methods and their computer implementation. We will concentrate on the areas that cause trouble in practice, including developing algorithms that converge from bad starting points, the approximation of derivatives when they aren't available analytically, and the solution of problems with large numbers of variables. The aim is to enable the student to solve these and related problems in real world situations, and to understand the methods involved.
Course outline : chapters 1-10 of text, plus lectures on global optimization, solution of large scale problems, and parallel optimization methods
Text : Numerical Methods for Unconstrained Optimization and Nonlinear
J. E. Dennis and R. B. Schnabel, SIAM, 1996
Reserve reading in math-physics library :
Practical Methods of Optimization, 2nd Edition, R. Fletcher, John Wiley and Sons, 1987
Practical Optimization, P. Gill, W. Murray, and M. Wright, Academic Press, 1981
The most effective method of communication is email. Please feel free to send questions or comments by email at any time, they will usually get a quick response, including on weekends and often in the evening as well. My responsibilities as associate vice chancellor for academic and campus technology mean that I will mainly be in my Regent Hall office or in meetings, and will be difficult to reach by phone or drop-in visits.
In order to avoid cancelling any classes due to unavoidable obligations from my administrative position, we will try to find a make-up class time that all students are able to make and that we can use as occasionally. If possible for all students, this will be Fridays from 2-3:15.