HYBRID PROJECTION ALGORITHM FOR SPLIT VARIATIONAL INEQUALITIES WITH MULTIPLE OUTPUT SETS IN HILBERT SPACES
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DOI:
https://doi.org/10.34238/tnu-jst.15221Abstract
In this paper, we study the split variational inequality problem with multiple output sets in real Hilbert spaces. This problem provides a unified framework that includes several important split models as special cases, such as the split feasibility problem, the split common minimum point problem, and the split common fixed-point problem with multiple output sets. To solve this problem, we propose a novel iterative algorithm that combines the hybrid projection technique with a multistep inertial extrapolation. The algorithm is designed with self-adaptive step sizes and control parameters, and therefore does not require any prior knowledge of the norms of the transfer operators. Under suitable assumptions, we prove that the sequence generated by the proposed algorithm converges strongly to a solution of the problem. Our results also extend and improve several existing works in the literature by removing the restrictive requirement to compute or estimate the norms of the transfer operators in previous algorithms.Downloads
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