General parameterized proximal point algorithm with applications in the statistical learning

In the literature, there are a few researches for the proximal point algorithm (PPA) with some parameters in the proximal matrix, especially for the multi-objective optimization problems. Introducing some parameters to the PPA will make it more attractive and flexible. By using the unified framework of the classical PPA and constructing a parameterized proximal matrix, in this paper, we design a general parameterized PPA with a relaxation step for solving the multi-block separable convex programming problem. By making use of the variational inequality and some mathematical identities, the global convergence and 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 show that our proposed algorithm can be very efficient and robust compared with some state-of-the-art algorithms.

Citation

J. Bai, et al. General parameterized proximal point algorithm with applications in the statistical learning. International Journal of Computer Mathematics, Accepted, 2017.

Article

Download

View General parameterized proximal point algorithm with applications in the statistical learning