Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions

Suthep Suantai, Suparat Kesornprom and Prasit Cholamjiak
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Suthep Suantai: Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Suparat Kesornprom: School of Science, University of Phayao, Phayao 56000, Thailand
Prasit Cholamjiak: School of Science, University of Phayao, Phayao 56000, Thailand

Mathematics, 2019, vol. 7, issue 8, 1-17

Abstract: We investigate the split variational inclusion problem in Hilbert spaces. We propose efficient algorithms in which, in each iteration, the stepsize is chosen self-adaptive, and proves weak and strong convergence theorems. We provide numerical experiments to validate the theoretical results for solving the split variational inclusion problem as well as the comparison to algorithms defined by Byrne et al. and Chuang, respectively. It is shown that the proposed algorithms outrun other algorithms via numerical experiments. As applications, we apply our method to compressed sensing in signal recovery. The proposed methods have as a main advantage that the computation of the Lipschitz constants for the gradient of functions is dropped in generating the sequences.

Keywords: split variational inclusion problem; compressed sensing; proximal algorithm; hilbert spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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