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.

Problem sets 30%
Midterm exam 30%
Final exam 40%


1 Formulations
2-4 Geometry
5-8 Simplex method
9-11 Duality theory
12 Sensitivity analysis
13 Robust optimization
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