Exact robust regression with applications to the control of weight filling machines

This thesis work addresses a class of optimization problems, that include, for instance, robust regression and support vector machines. These two subproblems belong to machine learning techniques and have very important industrial applications. In general, problems belonging to this class are not convex and NP-Hard. In this thesis, we propose an exact solution method based on a branch and bound approach. The method allowed us to device two novel algorithms for the solution of robust regression and, respectively, support vector machines. We applied the first algorithm to a real case study, consisting in the control of a weight filling machine. We theoretically proved the correctness of the proposed methods. Moreover, numerical experiments demonstrate the effectiveness of the procedures, that are particularly well suited to problems with few regressors and a large number of samples.