  In the literature, there are a few researches to design some parameters in
the Proximal Point Algorithm (PPA), especially for the multi-objective convex
optimizations. Introducing some parameters to PPA can make it more flexible and
attractive. Mainly motivated by our recent work (Bai et al., A parameterized
proximal point algorithm for separable convex optimization, Optim. Lett. (2017)
doi: 10.1007/s11590-017-1195-9), in this paper we develop a general
parameterized PPA with a relaxation step for solving the multi-block separable
structured convex programming. By making use of the variational inequality and
some mathematical identities, the global convergence and the worst-case
$\mathcal{O}(1/t)$ convergence rate of the proposed algorithm are established.
Preliminary numerical experiments on solving a sparse matrix minimization
problem from statistical learning validate that our algorithm is more efficient
than several state-of-the-art algorithms.
