Fall 2001

Professor Terry L. Friesz

tel: 703 993 1658    email:


HOMEWORK: Homework will be assigned and randomly graded; homework will be the primary source of questions for the exams. Following the due dates for homework assignments, solutions of most homework problems will be presented during the lectures.


EXAMS: Two midterms and a final exam. The exams will be in-class exams. See “Special Information” below.


PROJECT: Every student will be required to do a term paper or an approved project. The nature and details of this requirement will be described during the first lecture.


GRADING: Your homework will constitute 25% of you grade; each of the three exams will constitute 25%.


RECOMMENDED TEXT: The following text is recommended:


1.       Bhatti: Practical Optimization Methods, Springer, 2000 (isbn 0 387 98631 6)


RECOMMENDED SOFTWARE: You must acquire and learn how to use the linear and nonlinear mathematical programming utilities contained in one of the following commercial software packages:


1.       GAMS

2.       MATLAB

3.       AMPL

4.       MAPLE

5.       Scientific Work Place (


IMPRORTANCE OF LECTURES: Lectures will be the single most important source of information. The book will be used for suggested readings to reinforce the classroom presentation and sometimes as a source of homework, exam problems and the term paper/project. Although there are no explicit penalties for missing a lecture, experience has shown that students who miss the lectures are unable to fully comprehend the material and do extremely poorly on exams. Much of each classroom presentation is extemporaneous and geared to the particular difficulties of the class on the day of the lecture; as a consequence notes are of great importance.


SPECIAL INFORMATION: No makeup exams will be given, unless you have a written excuse approved by the Associate Dean (B. White). Such excuses are very seldom given. So don’t even think about asking for a make-up exam if you do not already have such written approval from the Associate Dean.


PREVIOUS COURSE EVALUATIONS: In Fall 1998 this course received an overall rating of 4.94; in Fall 1999 the rating was 4.65; in Spring 2001 the rating was 4.85. A summary of student evaluations may be found at






1.       Introduction                                                            

2.       Definition of a Mathematical Program            

3.       Optimality Defined                                                   

4.       Necessary and Sufficient Conditions 

5.       Algorithms for Unconstrained Nonlinear Programs

6.       Linear Programming Algorithms

7.       Algorithms for Constrained Nonlinear Programs

8.       Case Studies in Applications of Mathematical Programming

9.       Equilibrium Problems

10.    Case Studies in Equilibrium Modeling

11.    Optimal Control Problem Defined

12.    Necessary Conditions for Deterministic Optimal Control: The Minimum Principle

13.    Optimal Control Case Studies