The syllabus is the following:
- Operations Research Models
- Graphical solution of MP problem in two variables
- Convex and concave optimization
- Unconstrained optimization: first and second order optimality conditions. The gradient method
- Optimality conditions for inimization over a convex set. The conditional gradient method
- Equality constraied optimality conditions (Lagrange condition for linear constraints)
- Inequality Constrained optimization: optimality conditions in the case of linear constraints: the Karush-Kuhn-Tucker conditions (Alternative theorems: Farkas Lemma)
TO BE UPDATED BELOW
- Linear Programming Theory: vertex and main LP theorem
- Duality theory for LP: economic use of shadow prices
- Integer Linear Programming: connection LP and ILP (unimodularity); Branch and Bound algorithm
- Multiobjective optimization
For more details see the Lectures page.