A Family of Multi-Parameterized Proximal Point Algorithms

In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear convergence rate from the prospective of variational inequality. Preliminary numerical experiments on testing a sparse minimization problem from signal processing indicate that the proposed algorithm performs better than some well-established methods.