Department of Management Science and Engineering
Stanford University
Spring 2003
Solution of nonlinear equations; unconstrained optimization; linear
programming; quadratic programming; global optimization: general linearly
constrained optimization. Algorithms to solve the above problems. No
previous knowledge of optimization is required but a strong background in
analysis and numerical linear algebra is needed.
Course Staff
Instructor:Walter
Murray (walter@stanford.edu).
Room 327, Terman Engineering Center
(650) 723-1307
Office Hours: by appointment.
Teaching Assistant:Uday Shanbhag (udaybag@stanford.edu).
Room 329, Terman Engineering Center
(650) 725-8972
Office hours: Tuesday from 9:00 to 10:30am, in Terman 453.
Teaching Assistant:Lek-Heng Lim (lekheng@stanford.edu).
Room 284, Gates Building 2B
(650) 725-4163
Office hours: Monday from 2:30 to 3:30pm, in Terman 401.
Course topics
Solution of nonlinear equations
Unconstrained optimization
Nonlinear least-squares
Linear programming
Quadratic programming
Linearly constrained least-squares
General linearly constrained optimization
Global optimization
Grades and Assignments
Comprehensive notes will be provided. There is no exam. A grade will be
assessed on about eight homework sets and a MATLAB project. Homework will
be given on Wednesday and is due the following Wednesday. It is likely I
shall hold a homework workshop on Friday at the same time and place.
Homework Policy
Due in class on Wednesdays
One late homework is allowed without explanation.
Anyone wishing to be excused submitting additional homework on time
must do so at least one day prior to its due date.
Recommended Texts
P.E. Gill, W. Murray, and M.H. Wright, Practical
Optimization, Academic Press, London, 1986.
S.G. Nash and A. Sofer, Linear and Nonlinear
Programming, Mcgraw-Hill, New York, NY, 1996.
P.E. Gill, W. Murray, and M.H. Wright, Numerical
Linear Algebra and Optimization, Volume 1, Addison-Wesley,
Redwood City, CA, 1991.
P.E. Gill and W. Murray (Eds), Numerical Methods for Constrained
Optimization, Proceedings of a Symposium held at the National Physical
Laboratory, Teddington, January 10–11, 1974, Academic Press,
London, 1974.
D.G. Luenberger, Linear and Nonlinear Programming, 2nd
Edition, Addison-Wesley, Reading, MA, 1989.
R. Fletcher, Practical Methods for Optimization, 2nd
Edition, John Wiley, Chichester, 2000.
Final Part of the Project: I want you to use your quasi-Newton
code to solve the problem of how to distribute n points on a sphere
"uniformly". The definition of what is uniform may vary. The general
principle is that the points are not clustered . For example, if there
were two points, one would expect them to be placed at the poles. Try and
solve as large a problem as you can. You will need to submit a soft copy
of the code. However marks will not be awarded for smart coding. You will
need to describe the definition of your problem and your algorithm in
addition to the steps you took to develop the code in terms of the tests
you performed. Having obtained a "solution" you need to justify the claim
that it is a solution. You may also care to comment on the performance of
your algorithm.