A projective double inertial Ishikawa forward-backward splitting algorithm for variational inclusion problems with application to osteoporosis prediction

This work introduces a projective double inertial Ishikawa forward-backward splitting algorithm for solving variational inclusion problems in Hilbert spaces.We establish a weak convergence theorem under suitable control conditions, ensuring the reliability of the proposed approach.Numerical experiments, including an example in an infinite-dimensional space, demonstrate the algorithm's efficiency and validate the theoretical results.Furthermore, our study shows the effectiveness of applying the proposed algorithm to osteoporosis prediction using a multi-layer ELM, with the 2-layer ELM configuration achieving the highest performance across all metrics (accuracy, precision, recall, and F1-score), underscoring its robustness and efficiency.