Ricerc@Sapienza

Many problems arising in the fields of engineering, management, machine learning give rise to specific optimization problems. To solve these problems, algorithms must be designed which are tailored to the peculiarities of the problem itself. To solve such problems, two main classes of algorithms are to be considered.
- Derivative-free methods
- Methods for large-scale optimization

"Derivative-free methods"
These methods do not require the use of any analytical expression of the objective and constraint functions of the problem. They are the methods of choice to solve simulation based optimization problems. Those complex problems that are characterized by the fact that there exists only a ¿black-box¿ (i.e. a simulation tool or an approximation technique) which computes objective and constraint functions value. In recent years, many derivative-free methods have been proposed for the solution of simulation-based problems that present specific difficulties or peculiarities. Among such features, it can be mentioned the fact that the values of the objective and constraint functions can be computed with different precision (fidelity) or that they are affected by random noise (following an unknown probability distribution); furthermore, some (or all) of the variables could be restricted to take integer values.

"Methods for large-scale optimization"
These class of methods is devoted to the solution of large-scale problems, i.e. those problems that have an (extremely) high number of variables and/or constraint functions. The recent developments in the field of data mining and machine learning require us to be able to deal with large scale problems in which the particular structure of the objective function make them very difficult to minimize. The proposed activity will study truncated Newton-type methods and how they can be adapted to take into account the previous computational difficulties.