Relaxed Inertial Projective Forward-backward Splitting Algorithms for Regularized Least Square Problems

This study presents flexible conditions of the inertial extrapolation parameter for easy implementation that is added to the algorithm in faster convergence. Modified inertial forward-backward splitting algorithms for solving variational inclusion problems are introduced to apply to solve the LASSO problem for image restoration and signal recovery, and the elastic net model for classification problem. Projection methods are used in the final step for narrowing down the search field, resulting in a better solution.