- General parameterized proximal point algorithm with applications in the statistical learning Jianchao Bai (bjc1987163.com) Jicheng Li (jclimail.xjtu.edu.cn) Pingfan Dai (daipf2004163.com) Jiaofen Li (lixiaogui1290163.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. Download: [PDF]Entry Submitted: 03/12/2017Entry Accepted: 03/13/2017Entry Last Modified: 12/15/2017Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.