THE OBJECTIVE OF THE COURSE IS TO ENDOW THE STUDENTS WITH THE KEY ASPECTS OF DETERMINISTIC OPTIMIZATION, INCLUDING LINEAR AND NONLINEAR PROGRAMMING. TOPICS INCLUDE BASIC THEORY, MODELING, ALGORITHMS, AND APPLICATIONS.
teacher profile teaching materials
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
Programme
1. Introduction to Mathematical ProgrammingConvex 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 notesType of delivery of the course
Classroom lectures and exercises.Attendance
Classroom lectures and exercises.Type of evaluation
The exam consists of two steps. In the written part the student is asked to solve two exercises and answer a theoretical question. The oral part consists of one or more questions on the written part and/or theoretical questions. The exams of the last years are available on the web page of the course (http://pacciarelli.dia.uniroma3.it/CORSI/Ric_Op/Welcome.html ).