Computer Science 6676, Spring 1999                                         January 22, 1999

Assignment 1

Due Friday, February 5    (at beginning of class)

1. Chapter 1, problems 2, 3.
1. 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.]
1. 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.
1. Chapter 2, problems 3, 12, 15, 21.    (Note that convergence rate means the fastest rate that a sequence satisfies.)