Abstract
The split variational inclusion problem (SVIP) has been extensively studied and applied in real-world problems such as intensity-modulated radiation therapy (IMRT) and in sensor networks and in computerized tomography and data compression. Inspired by the works of L$\acute{o}$pez et al.$[24]$, Byrne et al.[10] and Sitthithakerngkiet et al.[34], as well as of Moudafi and Thukur[29], we propose a self-adaptive step size algorithm for solving split variational inclusion problem (SVIP) without the prior knowledge of the operator norms. Under more mild conditions we obtain weak convergence of the proposed algorithm. We also construct a self-adaptive step size two-step iterative algorithm which converges strongly to the minimum-norm element of the solution of the SVIP. Finally, the performances and computational examples are presented and a comparison with related algorithms is provided to illustrate the efficiency and applicability of our new algorithms.
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