Lecture Summaries  for COMP 566A                     Autumn 2005

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        Linear Programming, V. Chvatal

Sept 1    No class

Sept 6: Introduction to Mathematical Programming, and a quick outline of the history of Linear Programming. We discussed the fundamental contributions of George Dantzig,  and Leonid Khachiyan, both of whom passed away this year.

Sept 8: How to solve LPs in standard form. Read ch 2 of the text. Make up and solve one complete example by hand !

Sept 13: A formal statement of the simplex method. Dantzig and Bland's rule. Cycling and degeneracy. A geometric view of the simplex method. Read: text ch. 3 except pp 34-38.

Sep 15: Another simple and self contained way of getting a feasible solution to a system of inequalities was described. We proved finiteness and Farkas' lemma. Read:  notes.

Sept 20: Certificates for the 3 termination conditions. Unbounded solutions. Duality theory. Proof of the weak  duality theorems. Read:  Ch 5 up to p. 62 except proof of thm 5.1.

Sep 22: Proof of Strong duality theorem. Interpretation of dual variables. Read: Proof of Thm 5.1 and pp. 65-68.

Sep 27: Complementary slackness conditions. Formulation of 2-layer graph layout as an integer program. Read: pp 62-68 and for graph layout the paper of Junger et al.

Sep 29. The revised simplex method. Read text: Ch 7 to p. 105.

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