Prerequisites: Multivariable calculus (e.g. Math 175), linear algebra (e.g. Math 194, 204 or 205a) and a computer programming course (e.g. CS 101) are required.
Instructor: Mark Ellingham, SC 1514, phone 322 6670, email mark.ellingham at vanderbilt.edu.
Web page: http://www.math.vanderbilt.edu/~mne/287/.
Office hours: Tuesday, Wednesday and Thursday, 12:00 noon - 1:00 p.m.
Classes: Tuesday and Thursday, 9:35-10:50 a.m., SC 1432.
Textbook: I have not been able to find a book that covers all the course material at an appropriate level. Lecture notes and other handouts may be available for some of the material but students should expect to rely on their class notes much of the time.
References: The following books are useful general references for nonlinear optimization:
Assessment for this course will consist of four
parts: written problems, a project, one
midterm test, and a final examination. Your final grade will be
calculated from a percentage calculated as follows.
Written problems: Problems will be assigned on a regular basis during class, and (unless a different schedule is announced in class) will be due in class on the Thursday of the school week following the week in which they are announced. If you have a good reason for submitting an assignment late, please see me (in advance if at all possible) to make arrangements. Otherwise, late assignments will receive a mark of zero.
Written solutions to problems should be fully explained, using clear English sentences where necessary. Solutions should be written neatly on one side only of clean paper with straight (not ragged) edges. Multiple pages should be stapled (not clipped or folded) together.
Some problems will require the use of a computer algebra system, specifically Mathematica.
Practice problems: Problems for practice will be given out on a regular basis, and will be discussed in class as time permits.
Project: Students will be required to complete a project, which may take one of two forms: a paper on an application of optimization theory, or a computer project involving implementation of an optimization method. Projects may be done individually or in pairs. The descriptions below are for individual projects; more is expected from pairs. A proposal for the project, worth 2% of the final grade, will be due about six weeks into the semester; the project itself, worth 13% of the final grade, will be due towards the end of the semester.
The paper should concern an application of optimization theory (preferably nonlinear, but linear optimization may be allowed if you discuss the situation with me), either to a real-world problem or to another mathematical problem. It should be about twelve to sixteen pages in length.
The computer project can involve the implementation of either a basic optimization method in the context of some particular application, or an advanced method in an abstract setting. Any computer language that is appropriate may be used. Software written by other people (e.g. subroutine libraries) may be used as part of the infrastructure for a project. The project must be accompanied by a short (five pages or so) writeup describing the purpose of the code, and how to run it. Examples of output, and a demonstration of the running project, will be required.
Midterm test and final examination: There will be one 75-minute in-class test, which will be announced at least one week in advance. (A likely date is Thursday, 28th February, immediately before Spring Break.) Absence from the test will be excused only if authorized in advance by the instructor. In case of an emergency the instructor must be notified before the test begins -- if you cannot reach me, leave a message with the Math office (322 6672). If sufficient notice of an absence is given, arrangements will be made for you to take the test early. If this is not possible your final mark at the end of the semester will be prorated to take into account the missed test. Absolutely no makeups will be given after the test. In the event of an unexcused absence, or if the instructor is informed unreasonably late of a forseeable absence, then the mark for the test will be recorded as zero.
There will be a 120-minute final examination at 3 p.m. on Thursday, 2nd May. I have not yet decided whether to give an alternate examination. If there is an alternate examination it will be at noon on Friday, 26th April.
Both the test and the final examination will contain questions involving proofs, essays, or both, as well as questions requiring computations.
Honor code: The Vanderbilt Honor Code applies as follows. Work on written problems to be submitted, the test or the final examination must be done individually; you may not obtain assistance from any source, with the exception of hints given by the instructor. You may discuss your work on the project with others, but the final project must be your own work.
Drop dates: The drop-add period ends on Monday, 14th January. The last day to withdraw from the course is Friday, 15th March.