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 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.
Acknowledgements
The authors wish to thank the Editor-in-Chief Prof. Choi-Hong Lai and the anonymous referees for providing their valuable suggestions, which have significantly improved the quality of our paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. http://web.stanford.edu/∼boyd/papers/admm/covsel/covsel_example.html.