Programme

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

Core Documentation

Lecture notes

Type of delivery of the course

Classroom lectures and exercises.

Type of evaluation

Verification of learning takes place through a selective written test, lasting 90-120 minutes, aimed at verifying the level of actual understanding of the concepts learned in the course and the students' ability to apply them in real contexts. The course also includes an optional written test, which is held after the first part of the course, consisting of two exercises and a theory question, aimed at verifying the level of learning after the first part of the course. The expected time is 90-120 minutes. The exam consists of a written test, consisting of two compulsory exercises and a theory question divided into open-ended points. The expected time is 90-120 minutes. The exam texts of the last years are available on the course website (http://pacciarelli.dia.uniroma3.it/CORSI/Ric_Op/Welcome.html ).