Computer Science 6676, Spring 1999
January 22, 1999
Due Friday, February 5 (at beginning of class)
Chapter 1, problems 2, 3.
Calculate machine epsilon on the computer and precision that you are
likely to use for the class project, using the simple algorithm given in
class (or see Chapter 1, problem 7). What is the value that you get as
a power of 2, and as a decimal number? Is this the "correct"
value for the computer and precision you are using? If not, do you know
why not? [Reminder: please use IEEE double precision or the rough equivalent.]
Find an article or report that describes, in some detail, the formulation
of a "real" continuous optimization problem, either unconstrained
optimization, constrained optimization, or nonlinear equations. (Among
the possible sources for finding such a paper may be optimization journals,
other numerical computation journals, or engineering or science journals.
Some possible articles will be mentioned in class.) Read at last enough
of the article to understand what the application problem is, how it is
modeled, what sort of optimization problem this leads to, and what interesting
challenges for optimization algorithms this leads to (if this is described
in the paper). Submit a 1-2 page report (single spaced computer written,
or the equivalent) that names the article you read and summarizes the issues
mentioned above, and other aspects of the article that you found particularly
interesting, if any. (Various articles are likely to go into various levels
of depth in actually describing the mathematical model of the application.
Among the aspects of the model that you should report are what sorts of
equations are involved in calculating the function and constraints, and
what the optimization parameters are.) Note: The purpose of this exercise
is for you to become acquainted with an application that leads to an optimization
problem, preferably one that interests you. The main purposes of the report
are to confirm that you have done this and for me to learn something from
what you have read. It is not necessary for the report to be polished,
nor will it be be graded in a detailed manner.
Chapter 2, problems 3, 12, 15, 21. (Note that
convergence rate means the fastest rate that a sequence satisfies.)