Journal
NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION
Volume 13, Issue 2, Pages 273-298Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/naco.2022007
Keywords
Variational Inequality Problems; Halpern Subgradient Extragradient Algorithms; Parallel Self-adaptive Algorithms; Common Fixed Point Problems; Multiple Sets Split Variational Inequality Problems.
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In this paper, we extend a class of split variational inequality problem and fixed point problem to a class of multiple sets split variational inequality problem and common fixed point problem in Hilbert spaces. We propose a parallel Halpern subgradient extragradient CQ-method with adaptive step-size for solving the CMSSVICFP. The convergence of the proposed algorithm to the solution of the CMSSVICFP is demonstrated. Numerical tests validate the efficiency of our method.
In this paper, we present extension of a class of split variational inequality problem and fixed point problem due to Lohawech et al. (J. Ineq Appl. 358, 2018) to a class of multiple sets split variational inequality problem and common fixed point problem (CMSSVICFP) in Hilbert spaces. Using the Halpern subgradient extragradient theorem of variational inequality problems, we propose a parallel Halpern subgradient extragradient CQ-method with adaptive step-size for solving the CMSSVICFP. We show that a sequence generated by the proposed algorithm converges strongly to the solution of the CMSSVICFP. We give a numerical example and perform some preliminary numerical tests to illustrate the numerical efficiency of our method.
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