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 mo...
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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 caseO(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.
This paper presents two proximal-based pre-correction decomposition methods for convex minimization problems with separable *** methods,derived from Chen and Teboulle’s proximal-based decomposition method and He’s p...
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This paper presents two proximal-based pre-correction decomposition methods for convex minimization problems with separable *** methods,derived from Chen and Teboulle’s proximal-based decomposition method and He’s parallel splitting augmented Lagrangian method,remain the nice convergence property of the proximal point method and could compute variables in parallel like He’s method under the prediction-correction *** results are established without additional *** the efficiency of the proposed methods is illustrated by some preliminary numerical experiments.
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