MATH 305

Optimization

Instructor:

Assoc. Prof. Dr. Murat Adývar

Office:

Room: 424

Office Hours:

Tue 14:30-17:30 (or by appointment via e-mail)

e-Mail:

murat.adivar@ieu.edu.tr

Phone:

(232) 488 83 77

Class Hours:

Wednesday 08:30-12:20                                                 Classroom: C 403

Announcements:

 

Announcements will be given in class and posted to the course web site. Students should regularly check the web site for new and updated announcements.

Objectives:

This course aims to provide a deep understanding of standard techniques of linear optimization. After taking this course you will gain an aiding tool for solving real-world problems which require linear programming (LP) approach. The objective of this course is to cover fundamental topics of LP such as Graphical method, Enumeration method, Simplex method, Interior point method, Karmarkar’s projective scaling method, and Affine scaling method.

 

Course Outline:

1

Geometry of Linear Programming

 

2

The revised simplex method

 

3

Duality theory and sensitivity analysis

 

4

Complexity and ellipsoid method

 

5

Karmarkar’s projective scaling algorithm

 

6

Affine scaling algorithms

 

7

Insights into the interior-point methods

 

 

Textbook:

S. C. Fang & S. Puthenpura, Linear Optimization and Extensions: Theory and Algorithms, Prentice-Hall (1993).

 

Reference Books:

M. S. Bazaraa, J. J. Jarvis, and H. D. Sherali, Linear Programming and Network Flows, John Wiley, 2nd. Ed., New York (1990)

G. B. Dantzig, Linear Programming and extensions, Princeton University Press, Princeton, NJ, (1963)

Useful links:

   

You can find answers of FAQ about Linear /Nonlinear Programming via following links:

 

-         http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html

-         http://www-unix.mcs.anl.gov/otc/Guide/faq/nonlinear-programming-faq.html

Rererences for further reading:

 

Read the following four papers appeared in Operations Research, Vol. 50, No. 1, 2002:

 

  1. G.B. Dantzig - Linear Programming
  2. S.I. Gass - The First Linear Programming Shoppe
  3. R.E. Bixby - Solving Real-World Linear Programs: A Decade and More of Progress
  4. W.W. Cooper - A Brief History of a Long Collaboration in Developing Industrial Uses of LP

Assignments:

Homework and reading assignments will be given in class.

Evaluation:

Students will receive a final letter grade according to the scale shown below, formulated with the percentages in the below table. Performance shown in assignments, quizzes, exams and participation make up an important part of instructor's final opinion.

 

Grading

Percent

Midterm

30

Final

40

Assignments

20

Attendance&Participation

10

Attendance:

Attendance is required at all times. Students are expected to come to class fully prepared to discuss textbook readings and course assignments.