On the convergence and applications of the inertial-like method for null-point problems
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In this paper, we propose two novel inertial-like algorithms for solving the split common null point problem (SCNPP) with respect to set-valued maximal operators. The features of the presented algorithm are using new inertial structure (i.e, the design of the new inertial-like method does neither involve computation of the norm of the difference between x_n and x_n-1 in advance, nor need to consider the special value of the inertial parameter θ_n to make the condition ∑_n=1^∞α_nx_n-x_n-1^2<∞ valid) and the selection of the step-sizes does not need prior knowledge of operator norms. Numerical experiments are presented to illustrate the performance of the algorithms.
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