Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Recitations: 1 session / week, 1 hour / session
Course Content
This course is an introduction to linear optimization and its extensions emphasizing the underlying mathematical structures, geometrical ideas, algorithms and solutions of practical problems. The topics covered include: formulations, the geometry of linear optimization, duality theory, the simplex method, sensitivity analysis, robust optimization, large scale optimization network flows, solving problems with an exponential number of constraints and the ellipsoid method, interior point methods, semidefinite optimization, solving real world problems problems with computer software, discrete optimization formulations and algorithms.
Course Requirements and Grading
Grades will be determined by performance on the following requirements. Weights are approximate, and class participation is an important tie breaker.
| ACTIVITIES | PERCENTAGES |
|---|---|
| Problem sets | 30% |
| Midterm exam | 30% |
| Final exam | 40% |
Calendar
| LEC # | TOPICS |
|---|---|
| 1 | Formulations |
| 2-4 | Geometry |
| 5-8 | Simplex method |
| 9-11 | Duality theory |
| 12 | Sensitivity analysis |
| 13 | Robust optimization |
| Midterm | |
| 14-15 | Large scale optimization |
| 16-17 | Network flows |
| 18 | The Ellipsoid method |
| 19 | Problems with exponentially many constraints |
| 20-22 | Interior point methods |
| 23 | Semidefinite optimization |
| 24-25 | Discrete optimization |
| Final exam |