OR 644
Nonlinear Programming
Spring 2007,
Tuesday 4:30-7:10,
Robinson B124
Professor
Ariela Sofer
Science and Technology II, Room 111
phone: (703) 993-1692 or 993-1670 (secretary)
Office hours: Tuesday 2:30-4:00, Wednesday 1:30--3:00, or by
appointment
electronic mail: asofer@gmu.edu
fax: (703) 993-1521 (on cover sheet put: A. Sofer, SEOR Dept.)
Text
Stephen G. Nash and Ariela Sofer,
Linear and Nonlinear Programming,
McGraw-Hill, (1996).
Note: The book is temporarilly out of print. You may still get
some copies over the internet. Alternatively I will make copies of the
chapters that we will need. Students who use this option will have to
pay for the cost of the copying. (Buying the book is the better deal.)
Course description
Nonlinear programming problems arise in a wide variety of
applications, such as engineering design, finance, energy modeling, and
medical diagnosis and treatment. 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 software itself can be
downloaded here.
Throughout the course we might also experiment with the
modeling language AIMMS
A variety of nonlinear solvers may be accessed via the internet
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.
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
Class Schedule
Exam Dates
Midterm: Tuesday, March 27
Final exam due: Tuesday May 8, 5:00 pm
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.)