INFT 884/CSI 991:
Advanced Nonlinear Programming
Fall 1998
Tuesday 4:30-7:10,
Professor
Ariela Sofer
Science and Technology II, Room 123
phone: (703) 993-1692
office hours: Monday 5:00-6:30, Tuesday 3:00-4:00, or by appointment
electronic mail: asofer@gmu.edu
fax: (703) 993-1521 (on cover sheet put: A. Sofer, ORE Dept.)
Course Materials
Stephen Nash and Ariela Sofer,
Linear and Nonlinear Programming,
McGraw-Hill Book Publishing Company, 1996,
plus a selection of articles from the professional literature.
Optional Text
The Student Edition
of Matlab 5, Prentice Hall. The book comes in both a Windows CD-ROM
version or a Macintosh CD-ROM Version.
Course Description
This course will focus on theory and methods for constrained nonlinear
optimization. A key theme of the course will be the role of
duality in constrained optimization. We shall see that for many nonlinear
problems it is possible to define a related ``dual problem."
The theory of duality may be exploited to obtain faster and more effective
algorithms to solve the problem.
The early part of the course will focus on theroretical issues.
After a short review of unconstrained
optimization, we shall study the optimality conditions for
constrained optimization and introduce the concept of duality. Using
these tools we shall discuss methods for solving constrained
optimization problems. The focus will be on interior point methods, a
family of methods that has received much attention in recent years.
The discussion will include: barrier and penalty methods,
augmemted Lagrangian and modified barrier methods, and primal/dual
methods. Our final
topic will be semidefinite programs, which are optimization problems
where the unknowns are matrices rather than vectors.
Grading
In addition to to the material presented in class lectures, students will
be required to study via independent reading. Homeworks will be
assigned, and will address both the material covered in class, and
the material covered by the reading assignments.
Some assignments will require the development of Matlab code,
and/or the use of nonlinear programming software packages.
The homework assignments will contribute 70% of the course grade.
In addition there will be a take-home final exam
that will contribute 30% of the grade.
Other Information
Getting a computer account
SITE Computer Labs
(schedules, software, etc.)