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General parameterized proximal point algorithm with applications in the statistical learning

Jianchao Bai (bjc1987***at***163.com)
Jicheng Li (jcli***at***mail.xjtu.edu.cn)
Pingfan Dai (daipf2004***at***163.com)
Jiaofen Li (lixiaogui1290***at***163.com)

Abstract: 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.

Keywords: Convex programming; Proximal point algorithm; Relaxation step; Variational inequality; Complexity; Statistical learning

Category 1: Convex and Nonsmooth Optimization

Category 2: Applications -- Science and Engineering (Statistics )

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

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Entry Submitted: 03/12/2017
Entry Accepted: 03/13/2017
Entry Last Modified: 12/15/2017

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