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Several Variants of the Primal-Dual Hybrid Gradient Algorithm with Applications

Several Variants of the Primal-Dual Hybrid Gradient Algorithm with Applications
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Year:    2020

Author:    Jianchao Bai, Zhie Wu, Jicheng Li, Zhie Wu

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 1 : pp. 176–199

Abstract

By reviewing the primal-dual hybrid gradient algorithm (PDHG) proposed by He, You and Yuan (SIAM J. Image Sci., 7(4) (2014), pp. 2526-2537), in this paper we introduce four improved schemes for solving a class of saddle-point problems. Convergence properties of the proposed algorithms are ensured based on weak assumptions, where none of the objective functions are assumed to be strongly convex but the step-sizes in the primal-dual updates are more flexible than the previous. By making use of variational analysis, the global convergence and sublinear convergence rate in the ergodic/nonergodic sense are established, and the  numerical efficiency of our algorithms is verified by testing an image deblurring problem compared with several existing algorithms.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2019-0030

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 1 : pp. 176–199

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Saddle-point problem primal-dual hybrid gradient algorithm variational inequality convergence complexity image deblurring.

Author Details

Jianchao Bai

Zhie Wu

Jicheng Li

Zhie Wu

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