CS 591 - Linear and Integer (Spring 2004)

K. Subramani LCSEE, West Virginia University, Morgantown, WV ksmani@csee.wvu.edu

1 Preview

This course is primarily intended for a graduate audience in the CSEE, IMSE and Mathematics Departments, although undergraduate students with adequate preparation in linear algebra will also benefit from this course. It will serve as a thorough introduction to the fundamentals of Linear and Integer Programming from both a theoretical and a practical perspective.

2 Pre-requisites

Exposure to Linear Algebra.

3 Logistics

1. Class Times Tu - Th 8 : 00 am − 9 : 15 am.

2. Location - 215 ESB.

3. Office Hours - By appointment.

4. Class URL: http://www.csee.wvu.edu/˜ ksmani/courses/sp04/lp/lp.html.

4 Syllabus sketch

1. Linear Algebra - Systems of Linear Equations, Vectors and Matrices, Determinants, Vector Spaces and Subspaces, Linear Transformations (3 Lectures).

2. Modeling - Standard forms of Linear and Integer Programs, Capturing of Real World problems through these programs. (1 Lecture).

3. Algorithms for Linear Programming - Fourier-Motzkin elimination, Simplex Method and Duality, Dual Simplex, Ellipsoid Algorithms and Projective Algorithms (8 Lectures).

4. Graphs and Networks - Shortest Paths, Minimum Spanning Trees, Minimum Cuts, Maximum Flows, Transportation Problems, Network Simplex (4 Lectures).

5. Polyhedral Theory - Polyhedra and Dimension, Describing polyhedra by facets, Describing Polyhedra by Extreme points and Extreme Rays, Polarity (4 Lectures).

6. Integer Lattices - The Euclidean Algorithm, Continued Fractions, Lattices and Hermite Normal Form, Reduced Bases (4 Lectures).

7. General Purpose Algorithms - Branch and Bound, Cutting Plane Theory (4 Lectures).

5 Material

There are a number of texts that provide adequate introductions to the analysis of algorithms. For the most part, material from [NW99] will be used; however, I shall occasionally discuss material from [Sch87] as well.

6 Assessment

1. Quizzes (2) - Two quizzes will be held; one on February 12 and the other on April 15. These quizzes will be in-class and closed book. Each quiz is worth 20% (for a total of 40%) of your grade.

2. Midterm - The midterm will be held on March 16. It is in-class, closed book and worth 30% of your grade.

3. Final - The final will be held on May 8, 15 : 00 − 17 : 00. It is in-class, closed book and worth 30% of your grade. (Tentative)

A maximum of 5 points is reserved for class performance, which includes regular attendance and participating in class discussions.

7 Grade Boundaries

1. A - ≥ 90

2. B - 75 − 89

3. C - 60 − 74

4. D - 50 − 59

5. F - 0 − 49

8 Social Justice Statement

West Virginia University is committed to social justice. I concur with that commitment and expect to foster a nurturing learning environment, based upon open communication, mutual respect and non-discrimination. Our University does not discriminate on the basis of race, sex, age, disability, veteran status, religon, sexual orientation, color or national origin. Any suggestions to further such a positive and open environment in this class will be appreciated and given serious consideration. If you are a person with a disability and anticipate needing any type of accommodation, in order to participate in this class, please advise me of the same and make appropriate arrangments with Disability Services (293 − 6700).

If you feel that you are being treated inappropriately or unfairly in any way, please feel free to bring your concerns to my attention; rest assured that doing so will not prejudice the grading process. In return, I expect you to behave professionally and ethically.

References

[NW99] G. L. Nemhauser and L. A. Wolsey. Integer and Combinatorial Optimization. John Wiley & Sons, New York, 1999.

[Sch87] Alexander Schrijver. Theory of Linear and Integer Programming. John Wiley and Sons, New York, 1987.