In this paper, we develop a Parameterized Proximal Point Algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case $O(1/t)$ convergence rate, where $t$ is the iteration number. By properly choosing the algorithm parameters, numerical experiments on solving sparse optimization problem arising from statistical learning show that our P-PPA could perform significantly better than other state-of-the-art methods, such as the Alternating Direction Method of Multipliers (ADMM) and the Relaxed Proximal Point Algorithm (R-PPA).
J.C. Bai, H.C. Zhang, J.C. Li, A parameterized proximal point algorithm for separable convex optimization. Optim. Lett. (2017) DOI:10.1007 /s11590-017-1195-9