Tseng Splitting Method with Double Inertial Steps for Solving Monotone Inclusion Problems

TL;DR

This paper introduces a novel Tseng splitting method incorporating double inertial steps and adaptive step sizes, enhancing the efficiency of solving monotone inclusion problems in Hilbert spaces.

Contribution

The paper proposes a new algorithm combining double inertial extrapolation and relaxation techniques for improved convergence in monotone inclusion problems.

Findings

Demonstrates the effectiveness of the method through numerical experiments

Shows improved convergence properties over existing methods

Validates theoretical results with practical performance data

Abstract

In this paper, based on a double inertial extrapolation steps strategy and relaxation techniques, we introduce a new Tseng splitting method with double inertial extrapolation steps and self-adaptive step sizes for solving monotone inclusion problems in real Hilbert spaces. Finally, several numerical experiments are provided to illustrate the performance and theoretical outcomes of our algorithm.