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 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

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).