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A Parameterized Proximal Point Algorithm for Separable Convex Optimization

Jianchao Bai (bjc1987***at***163.com)
Hongchao Zhang (zhc***at***lsu.edu)
Jicheng Li (jcli***at***mail.xjtu.edu.cn)

Abstract: 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).

Keywords: Separable convex programming Proximal point algorithm Global convergence Statistical learning

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

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

Citation: 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

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Entry Submitted: 02/10/2017
Entry Accepted: 02/10/2017
Entry Last Modified: 09/09/2017

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