Inertial methods for split common fixed point problems: application to binary classification in machine learning

Abstract

The aim of this paper is to introduce a new two-step inertial method for approximating a solution to a generalized split common fixed point problem, which is a unique solution to a variational inequality problem. We establish a strong convergence theorem for the sequence generated by the algorithm. We explore various special cases related to fundamental problems, including the split feasibility problem, the split common null point problem, and the constrained convex minimization problem. To demonstrate the efficacy and performance of our proposed algorithm, we apply it to a practical scenario involving support vector machines for binary classification. The algorithm is employed on diverse datasets sourced from the UC Irvine Machine Learning Repository, serving as the training set.