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

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 ${\sum }_{n=1}^{\infty }{\alpha }_n\Vert x_n-x_{n-1}{\Vert }^2<\infty$ 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.

29 pages, 8 figures

References in corpus (1)

• Fast inertial dynamics and FISTA algorithms in convex optimization. Perturbation aspects