|
Date |
Topic |
Homework Due |
| 1. |
We Jan 22 |
Introduction |
| 2. |
Fr Jan 24 |
Linear Programming Modeling |
| 3. |
Mo Jan 27 |
Transformations and Standard Form of LP |
| 4. |
We Jan 29 |
LP Dual |
| 5. |
Fr Jan 31 |
Linear, Affine and Convex Hulls |
HW# 1
|
| 6. |
Mo Feb 3 |
Basic Solutions of Linear Systems |
| 7. |
We Feb 5 |
Polyhedral Sets |
| 8. |
Fr Feb 7 |
Representation Theorem |
HW# 2
|
| 9. |
Mo Feb 10 |
Fundamental Theorem of LP |
| 10. |
We Feb 12 |
Algebraic Characterization of Basic Solutions |
| 11. |
Fr Feb 14 |
Derivation of the Simplex Algorithm |
| 12. |
Mo Feb 17 |
Initialization |
| 13. |
We Feb 19 |
Basis Updates (PFI, BTRAN, FTRAN) |
| 14. |
Fr Feb 21 |
LU Factorization & Gaussian Elimination |
HW# 3
|
| 15. |
Mo Feb 24 |
Pivoting Strategies & Error Control |
| 16. |
We Feb 26 |
Updating the LU Factorization |
| 17. |
Fr Mar 28 |
Pivoting Strategies & Fill-in Control |
| 18. |
Mo Mar 3 |
Pricing |
| 19. |
We Mar 5 |
Steepest Edge Simplex Algorithms |
| 20. |
Fr Mar 7 |
LP Duality and Parametric Analysis |
HW# 4
|
| 21. |
Mo Mar 10 |
Convergence of the Simplex Method |
| 22. |
We Mar 12 |
Generalized Upper Bounding |
| 23. |
Fr Mar 14 |
Stochastic Linear Programming |
HW# 5
|
| 24. |
Mo Mar 17 |
Benders Decomposition |
| 25. |
We Mar 19 |
Column Generation |
|
|
Take Home Exam # 1 distributed |
| 26. |
Fr Mar 21 |
Lagrangian Dual & Subgradient LP Methods |
|
|
Computational Project distributed |
| 27. |
Mo Mar 31 |
Take Home Exam # 1 solutions |
| 28. |
We Apr 2 |
Overview of Interior Point Methods |
| 29. |
Fr Apr 4 |
Moving through the Interior |
| 30. |
Mo Apr 7 |
Projection |
HW# 6
|
| 31. |
We Apr 9 |
Projective Scaling |
| 32. |
Fr Apr 11 |
Karmarkar's LP |
| 33. |
Mo Apr 14 |
Karmarkar's Algorithm |
| 34. |
We Apr 16 |
Karmarkar's Algorithm |
| 35. |
Fr Apr 18 |
Proof of Polynomiality |
| 36. |
Mo Apr 21 |
Dealing with Unknown Optimal Value |
| 37. |
We Apr 23 |
Affine Scaling |
HW# 7
|
| 38. |
Fr Apr 25 |
Primal Affine Scaling |
| 39. |
Mo Apr 28 |
Potential Push Method |
| 40. |
We Apr 30 |
Dual Affine Scaling |
| 41. |
Fr May 2 |
Implementation Issues in Interior Point Methods |
HW# 8
|
| 42. |
Mo May 5 |
Semidefinite Programming |
|
|
Computational Project is due |
| 43. |
We May 7 |
Review |
|
|
Take Home Exam # 2 distributed |