Use Parallel Successive Convex Approximation (PSCA) algorithm for solving LASSO problem min_x 1/2 * |Ax - b|^2 + \lambda |x|_1
The details of PSCA algorithm can be found here: http://arxiv.org/abs/1406.3665
You can run the algorithm on your own data. For testing purposes, data can be generated by NesterovGenerateProblem.m