Approximate iterations in Bregman-function-based proximal algorithms

1998 ◽  
Vol 83 (1-3) ◽  
pp. 113-123 ◽  
Author(s):  
Jonathan Eckstein
Keyword(s):  
Proximal Algorithms ◽  
Bregman Function

scholarly journals Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 708 ◽  
Author(s):  
Suthep Suantai ◽  
Suparat Kesornprom ◽  
Prasit Cholamjiak
Keyword(s):  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Signal Recovery ◽  
Proximal Algorithms ◽  
Split Variational Inclusion Problem ◽  
Variational Inclusion Problem ◽  
Lipschitz Constants ◽  
Theoretical Results

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.

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