MODELLI MATEMATICI PER L'OTTIMIZZAZIONE

The objectives of the course Networks and Supernetworks are as follows:

• to determine paths of minimum and maximum length starting from a root node;
• to apply the concepts of generalized derivatives to functions;
• to apply the Lagrange theory to constrained optimization problems;
• to formulate an equilibrium problem as an evolutionary variational inequality;
• to solve evolutionary variational inequalities.

Knowledge and understanding: the aim of the course is to be able in recognizing constrained optimization problems and in formulating real life problems in mathematical terms

Applying knowledge and understanding: students will be able to identify the functional characteristics of the data, to analyze various optimization situations, to propose optimal solutions to complex problems.

Making judgments: students will be able to analyze the data.

Communication skills: students will be able to communicate their experience and knowledge to other people.

Learning skills: students will have acquired the ability to learn, even autonomously, further knowledge on the problems related to applied mathematics.

The course will be taught through lectures and exercises in the classroom and at the computer labs.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.

Learning assessment may also be carried out on line, should the conditions require it.

Graph theory (about 12 hours):

Graphs and digraphs: Definitions and preliminary notions, associated matrices. Kruskal's algorithm and its variant. Dijkstra's algorithm and its variant. Ford algorithm. Bellman-Kalaba’s algorithm. The traveling salesman problem.

Generalized derivatives (about 10 hours)

Directional derivatives, Gâteaux and Fréchet derivatives. Subdifferential.

Computational methods (about 8 hours)

The subgradient method. The discretization method.

Network models (about 17 hours)

Traffic networks. The Braess' paradox. Efficiency measure of a network. Supernetworks with three levells of decision-makers.

1. L. Daboni, P. Malesani, P. Manca, G. Ottaviani, F. Ricci, G. Sommi, “Ricerca Operativa”, Zanichelli, Bologna, 1975.
2. P. Daniele, “Dynamic Networks and Evolutionary Variational Inequalities", Edward Elgar Publishing, 2006.
3. J. Jahn, "Introduction to the Theory of Nonlinear Optimization", Springer, 1996.
4. Papers on STUDIUM http://studium.unict.it