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arXiv · 1812.03763

General parameterized proximal point algorithm with applications in statistical learning

Jianchao Bai·Jicheng Li·Pingfan Dai·Jiaofen Li
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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 $\mathcal{O}(1/t)$ convergence rate of the proposed algorithm are established. Preliminary numerical experiments on solving a sparse matrix minimization problem from statistical learning validate that our algorithm is more efficient than several state-of-the-art algorithms.

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Jianchao Bai, Jicheng Li, Pingfan Dai, Jiaofen Li. 2018-12-10. General parameterized proximal point algorithm with applications in statistical learning. https://doi.org/10.1080/00207160.2018.1427854

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