An iterative reduction fista algorithm for large-scale lasso

In this paper, an easy to implement and efficient algorithm is proposed for large-scale sparse least squares problems. It reduces the original large-scale problem into a sequence of small-scale subproblems by utilizing the "sparsity" of the gradient. A well-designed FISTA algorithm is presented to solve the subproblems. With the desired termination criterion, the algorithm is proved to globally converge and converge locally at linear rate. Moreover, a complexity of O(mp In 1/epsilon) is given for the presented algorithm. Numerical comparisons between the presented algorithms and a number of state-of-the-art algorithms on solving LASSO problems with large-scale LIBSVM data sets and image deblurring problems demonstrate the robustness and high performance of the presented algorithms. As an example, the presented algorithm only needs 9 seconds to solve a LASSO problem with 19,264,097 samples and 29,890,095 features.