Several self-adaptive inertial projection algorithms for solving split variational inclusion problems

TL;DR

This paper introduces several self-adaptive inertial projection algorithms for split variational inclusion problems in Hilbert spaces, demonstrating their convergence and effectiveness through theoretical analysis and experimental comparison.

Contribution

It proposes new inertial hybrid and shrinking projection algorithms with self-adaptive stepsizes that do not require operator norm information, advancing solution methods for split variational inclusion problems.

Findings

Algorithms converge strongly under mild conditions

Self-adaptive stepsizes improve algorithm robustness

Experimental results outperform existing methods

Abstract

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed under the effect of self-adaptive stepsizes which does not require information of the norms of the given operators. Some strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, an experimental application is given to illustrate the performances of proposed methods by comparing existing results.