A bi-inertial Mann projective forward-backward splitting algorithm for variational inclusion problems with application to lung cancer screening

This paper proposes a bi-inertial Mann projective forward-backward splitting algorithm to solve the variational inclusion problem in real Hilbert spaces. We establish a weak convergence result under mild conditions commonly used in convergence analysis. Additionally, we present a series of numerical experiments to demonstrate the efficiency of our algorithm compared to existing methods. Finally, we applied our algorithm to classify data using the lung cancer dataset, achieving the highest testing accuracy of 90.32\%, surpassing other documented algorithms. Our results indicate that the proposed algorithm offers a practical solution for detecting lung cancer.