Combinatorial Optimization

K. Subramani, LCSEE, West Virginia University January 28, 2013

1. Linear Programming forms.

2. Extreme points.

3. Fourier-Motzkin elimination.

4. Infeasibility in linear systems of equalities (certificates).

5. Weyl’s theorem.

6. Infeasibility in linear systems of inequalities.

7. Angle between two vectors. Determined through dot product.

8. Farkas’ Lemma.

9. Linear Programming duality. (Columns in one, become rows in the other).

10. Example that describes its motivation.

11. Various forms.

12. Weak duality theorem.