A random active set method for strictly convex quadratic problem with simple bounds

The active set method aims at finding the correct active set of the optimal solution and it is a powerful method for solving strictly convex quadratic problems with bound constraints. To guarantee the finite step convergence, existing active set methods all need strict conditions or some additional strategies, which can significantly impact the efficiency of the algorithm. In this paper, we propose a random active set method that introduces randomness in the active set’s update process. We prove that the algorithm can converge in a finite number of iterations with probability one, without any extra conditions on the problem or any supplementary strategies. At last, numerical experiments show that the algorithm can obtain the correct active set within a few iterations, and it has better efficiency and robustness than the existing methods.