AN ADAPTIVE BLOCK ITERATIVE PROCESS FOR A CLASS OF MULTIPLE SETS SPLIT VARIATIONAL INEQUALITY PROBLEMS AND COMMON FIXED POINT PROBLEMS IN HILBERT SPACES

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.

Automated summary

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.