Convergence of inertial hybrid splitting algorithms

1Semenov, VV
1V.М. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2018, 12:30-36
https://doi.org/10.15407/dopovidi2018.12.030
Section: Information Science and Cybernetics
Language: Russian
Abstract: 

Two new algorithms for solving the operator inclusion problems with maximal monotone operators acting in a Hilbert space are proposed. Algorithms are based on the inertial extrapolation and three well-known methods: Tseng forward-backward splitting algorithm and two hybrid algorithms for the approximation of fixed points of nonexpansive operators. Theorems on the strong convergence of the sequences generated by the algorithms are proved.

Keywords: Hilbert space, hybrid algorithm, inertial method, maximal monotone operator, operator inclusion problem, strong convergence, Tseng algorithm
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