The research activity will be devoted to the definition of new methodologies for solving two classes of difficult nonlinear optimization problems deriving from important real-world problems.

The first class consists of problems where the analytic expressions of the objective and the constraints functions are unknown and their values are obtained by direct measurements or by using complex approximations or simulation programs. Therefore for such problems no first order information is available. From the methodological point of view, the aim of the research is the definitions of derivative-free methods for difficult optimization problems such as constrained global multiobjective optimization problems, nonlinear mixed optimization problems, nonsmooth optimization problems, problems where the objective function and the constraints can be approximated with a variable precision. In the practical part of the activity some of the new algorithms will be used for tackling difficult real problems deriving from optimal designs of electrical motors, optimal designs of electrical magnetic apparatus, optimal ship design problems, managements of healthcare services, workforce management, definitions of optimal trading strategies.

The second class considered consists of problems which have the difficulty of having an extremely large number of variables and constraints of the problems and, in some cases, also an extremely large number of terms in the objective function. The methodological part of the research will consider the definition of new truncated Newton methods or Frank-Wolfe type algorithms for large scale unconstrained nonlinear optimization problems or large scale simple constrained nonlinear optimization problems and new Newton-Type algorithms for large scale constrained nonlinear optimization problems. Then some of these new algorithms will be used for solving particular optimization problem arising in the machine learning and the data mining fields.