- Linear programs: their basic properties; the simplex algorithm.
- Duality: the relationship between a linear program and its dual, duality theorems, complementarity, and the alternative; sensitivity analysis.
- The interior point method for convex optimization: optimality conditions; the central path; convergence analysis; applications to linear programming and general convex optimization.
- Integer Programming: Branch and bound algorithms and/or cutting plane methods.
- The use of a computer software to solve mathematical programming problems.