On the convergence and applications of the inertial-like method for null-point problems

Yan Tang; Shiqing Zhang

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arXiv · 2109.09082

On the convergence and applications of the inertial-like method for null-point problems

Yan Tang·Shiqing Zhang

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Abstract

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 $\theta_n$ to make the condition $\sum_{n=1}^\infty \alpha_n\|x_n-x_{n-1}\|^2<\infty$ 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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Yan Tang, Shiqing Zhang. 2021-09-19. On the convergence and applications of the inertial-like method for null-point problems. https://arxiv.org/abs/2109.09082

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