OR 644/MATH 689
Nonlinear Programming
Spring 2001,
Thursday 4:30-7:10, Krug Hall 2007
Professor
Ariela Sofer
Science and Technology II, Room 123
phone: (703) 993-1692 or 993-1670 (secretary)
Office hours: Monday 5:00--6:30, 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).
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
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 the AMPL book 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.
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 15
Final exam due: Thursday May 3, 5:00 p.m.
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.)