A novel parameterized proximal point algorithm with applications in statistical learning

In the literature, there are a few researches for the proximal point algorithm (PPA) with some parameters designed in the metric proximal matrix, especially for the multi-objective optimization problems. Introducing some parameters to the PPA can make it more attractive and flexible. By using the unified framework of the classical PPA and constructing a parameterized proximal matrix, in this paper, we develop a general parameterized PPA with a relaxation step for solving the multi-block separable convex programming problem. By making use of the variational inequality and some mathematical identities, the global convergence and worst-case O(1/t) convergence rate of the proposed algorithm are established. Some preliminary numerical experiments on solving a sparse matrix minimization problem from statistical learning show that our new algorithm can be very efficient and robust compared with some state-of-the-art algorithms.