OR 644 Nonlinear Programming

Spring 1998
Thursday 4:30-7:10, Robinson A249

Professor

Ariela Sofer
Science and Technology II, Room 123
phone: (703) 993-1692 or 993-1670 (secretary)
Office hours: Tuesday 3:30--5:00, Thursday 2:30--4:00, or by appointment
electronic mail: asofer@gmu.edu
fax: (703) 993-1521 (on cover sheet put: A. Sofer, ORE Dept.)

Text

Stephen G. Nash and Ariela Sofer, Linear and Nonlinear Programming, McGraw-Hill, (1996).

Optional text

Robert Fourer, David M. Gay and Brian W. Kernighan AMPL: A Modeling Language for Mathematical Programming, and AMPL Plus Student Edition for Microsoft Windows Duxberry Press/Brooks Cole Publishing Company, 1993.

Course description

Nonlinear programming problems arise in a wide variety of applications, such as engineering design, military planning, and energy modeling. This course provides an introduction to the theory and methodology of nonlinear programming. After a review of the required mathematical background, we will study the theory of unconstrained optimization. We will then discuss methods for minimizing unconstrained functions, including Newton's method, the steepest descent method, the conjugate gradient method and truncated Newton methods, and will discuss the merits and disadvantages of each of these methods. We will continue to study the theory of constrained optimization, and then discuss methods for constrained optimization, including active set methods and penalty and barrier methods.

Throughout this course we will solve a number of applied nonlinear programming problems using a variety of optimization software packages. The packages differ in the algorithm they use to solve the nonlinear programs, and one of our our goal will be to compare the performance of different algorithms on specific problems. The front end to these software packages will be the modeling language AMPL. The referenced optional text comes with a student version of AMPL for Windows, and includes a variety of optimization software including student versions of CPLEX, Minos, Conopt and GRG2. Other nonlinear solvers may be accessed via the internet through the NEOS Server. Many of these packages use AMPL as their front end. Students who do not wish to purchase AMPL may download a DOS version of the software. The DOS version does not include the optimization software packages, although various packages may be accessed through the NEOS server.

Grading

There will be an in-class midterm examination, and a take-home final. Each of these will be worth 25% of the grade. The midterm exam will be open book, open notes. B Homeworks will be assigned regularly in the first half of the semester, but only occasionally in the second half. Instead, students will have to complete two projects. These projects will involve solving via a variety of nonlinear optimization algorithms, using AMPL as the modeling language. The homeworks will make up 20% of the grade. and the two projects will make up 30% of the grade. In computing the final grade, the lowest homework grade will be dropped.

Homework to date

Exam Dates

Midterm: Thursday, March 19
Final exam due: Thursday, May 7.

Fundamental rules

Make-up exams will only be given for extreme situations, and only if I am contacted before the exam is given and full arrangements are established. Full adherence to this policy is the responsibility of the student.
The exam dates above are tentative, and it is the students responsibility to keep abreast of changes.
Homework will be assigned each class, and usually collected. All work must be clearly written. Illegible work will not be accepted.
There will be a penalty of 10% of the total grade for every day homework is late.

Other information

Getting a computer account

SITE Computer Labs (schedules, software, etc.)