A Two-Step Inertial CQ Method for Split Feasibility Problems with Applications

This paper introduces an algorithm for approximating solutions of split feasibility problems by employing a two-step inertial acceleration strategy along with a self-adaptive step size. This combination enhances the convergence rate and reduces computational complexity of the proposed algorithm. The nonasymptotic O(1/t) convergence rate and global convergence of the proposed method are established within the context of Euclidean spaces. The algorithm is extended to handle multiple set split feasibility problems, and a sensitivity analysis is conducted to identify optimal inertial parameter choices. Additionally, the algorithm is applied to the LASSO problem. Comparative evaluations with various algorithms from existing literature showcase the superior performance of the proposed algorithm.