Università Roma Tre

1. Introduction to Mathematical Programming
Convex Programming
Linear Programming
2. Linear Programming Formulation
Resource allocation
Inventory Management
Project planning
3. Solving Linear Programming Problems
Geometry of Linear Programming
The Simplex Algorithm
4. Duality Theory
The weak and strong duality theorems
Orthogonality conditions
Sensitivity analysis
5. Non-linear programming
Gradient, Hessian
Local minimum, Necessary conditions (first and second order)
Local minimum, Sufficient conditions (secondo order and convex case)
Gradient method, Line search
Newton method,
6. Constrained non-linear programming
KKT conditions
Barrier method and Penalty functions

Lecture notes