General parameterized proximal point algorithm with applications in statistical learning
Abstract
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 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.
Cite
@article{arxiv.1812.03763,
title = {General parameterized proximal point algorithm with applications in statistical learning},
author = {Jianchao Bai and Jicheng Li and Pingfan Dai and Jiaofen Li},
journal= {arXiv preprint arXiv:1812.03763},
year = {2018}
}