Lecture Summaries for COMP 566A
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Nov 4: More on zero sum games. Bimatrix games. Nash equilibria and
"generalized" complementary slackness
Oct 30: Matrix games. Read: Ch 15.
Second test will cover all material up to this point.
Oct 28: More on network simplex method. Initialization.
Integrality of LP solution. Finish Ch 19.
October 23: Network Simplex method. Start
reading Ch 19.
October 21: Dual simplex method and sensitivity
analysis. How to change c and b vectors, and add new variables and constraints.
Read: Ch 10 up to p.162 - you can skip revised dual simplex method.
October 16: Linear programming with bounds on the
variables. We used dictionaries, the book uses revised simplex method.
Read: Ch 8 up to p. 124
October 14: Class Test.
October 9: Efficient implementation of Revised
Simplex using Eta matrices. Economic interpretation of Revised Simplex.
Read: rest of Ch 7.
October 7: Revised Simplex Method. Read: Chapter
7 up to p. 105.
October 2: Infeasible problems. Certificate of infeasibility, and how
to compute it via Phase 1 of the simplex method.
We proved that Ax <= b, x>= 0 is infeasible
if and only if there is a dual vector y >= 0 s.t yA>=0
and yb < 0.
The proof is similar to the more general theorem
on pp 143-145.
Sept 30: Complementary Slackness Theorem and
proof using Duality Theorem . Economic interpretation.
solutions and their certificates.
Sept 25: Proof of Duality Theorem. Use as a certificate
of optimality. Complementary slackness. Read: rest of Chapter 5.
Sept 23: Dual linear program. Weak duality theorem
and proof. Statement of strong duality theorem. Read: pp. 54-62
Sept 18: Initialization and the two phase simplex
method. Read: Chapter 3
Sept 16: How good is the simplex method. Klee-Minty
examples. Read: Chapter 4
Sept. 11: General form of
dictionaries. Pivot selection rules. Cycling in the simplex method.
Read: Text Chapter 2 and pp. 31-32
Sept. 9: Saxby foods formulation. How to solve an LP from
Read: Text Chapter 1
Sept 4: Introduction to Operations
Research, Mathmetical Programming, Linear Programming and
Course outline and requirements. Buy text!