An inexact relaxed proximal point algorithm for multi-task sparse learning problem

The multi-task sparse learning problem has been very popular in many areas during the past several years. However, as a convex optimization problem, the multi-task sparse learning problem remains challenging because of large scale data and non-smooth properties. In this paper, we propose a proximal point algorithm (PPA) which can solve the wide applied multi-task sparse learning problems effectively. This approach is under the framework of variational inequalities, although it involves the projection-contraction technique and proximal-point technique respectively. Global convergence is obtained in a clear and concise way. The efficiency of the algorithm is shown in the numerical experiment part by comparing with other state-of-art methods.