An Improved Iterative Reduction FISTA-Barzilai-Borwein Algorithm for Large-Scale LASSO

The iterative reduction FISTA algorithm (IR-FISTA-B) is an extremely excellent algorithm for solving large-scale LASSO problems. It utilizes the sparsity and gradient of the solution to transform large-scale problems into small-scale subproblems, and uses the FISTA algorithm to solve subproblems. In this paper, we improve the algorithm by using the Barzilai-Borwein step size as the step factor in the inner loop algorithm, and provide appropriate parameter update criteria to accelerate the convergence rate of the algorithm. Under the ideal termination criterion, we prove that the algorithm converges to a minimum with a locally linear rate. In numerical experiments, the performance of the proposed algorithm for solving large-scale LASSO problems was demonstrated by testing on synthetic data and LIBSVM datasets comparing with the original algorithm.