MATHEMATICAL METHODS FOR OPTIMIZATION

The course aims at presenting the basic concepts of optimization. The course provides students with the analytic tools to model and foresee situations in which a single decision-maker has to find the best choice. The attention focuses on applications in economics, engineering, and computer science. The students will be also able to solve numerically the problems using the AMPL code.

The goals of the course are:

1. Knowledge and understanding: the aim of the course is to acquire base knowledge that allows students to understand optimization problems.
2. Applying knowledge and understanding: students will acquire knowledge useful to model real-life optimization problems.
3. Making judgments: through real examples, the student will be able to implement in AMPL correct solutions for complex decisional problems.
4. Communication skills: students will acquire base communication skills using technical language.
5. Learning skills: the course provides students with theoretical and practical methodologies in order to deal with several optmization problems that can meet during the work activity.

For this course, there will be both classroom lessons and laboratory lessons.

During the month of April, a midterm examination will be proposed via a 2-hour written paper. It corresponds to half-part of the program (4,5 CFU). It should be noted that this exam is not compulsory.

The course deals with linear and nonlinear optimization problems from both the theoretical and the computational point of view. The following issues will be presented:

convex sets, supporting hyperplanes, cones, tangent cones

convex and quasi-convex functions

optimality conditions, duality

algorithms for non linear problems

multiobjective optimization

AMPL implementations

1. I. Capuzzo Dolcetta, F. Lanzara, A. Siconolfi, Lezioni di ottimizzazione - Nuova Cultura, 2013
2. R. Tadei, F. Della Croce, A. Grosso, “Fondamenti di Ottimizzazione”, Società Editrice Esculapio, 2005;
3. M. Bruglieri, A. Colorni, “Ricerca Operativa”, Zanichelli, 2012;
4. F. Fumero, Metodi di ottimizzazione. Esercizi ed applicazioni - Esculapio, 2013 ​
5. R. T. Rockafellar, R. J-B Wets, Variational Analysis
6. S. Boyd, L. Vandenberghe, Convex optimization
7. J. Jahn, Introduction to the Theory of Nonlinear Optimization - Springer- Verlag, Berlin (1996).