We address a problem of a large-scale Quadratic Programming (QP) optimization. This type of optimization problems occurs, e.g., in machine learning or control theory. Conventional optimization methods become infeasible for problems with the number of variables exceeding several thousands. It will be shown that special instances of the large-scale QP tasks can be solved based on simple algorithms from computational geometry. In particular, we employ the methods for the Minimal Norm Problem and the Nearest Point Problems. The applications of the proposed QP solvers to problems from machine learning will be discussed.