User Manual FPC AS A MATLAB Solver for l1-Regularized Least Squares Problems

where x ∈ R, A ∈ R, M ∈ R, and b ∈ R, and μ > 0 is the regularization parameter. It is based upon the active-set algorithm with a continuation strategy described in [1, 2]. FPC AS is a successor of FPC [3]. While FPC AS still performs shrinkage iterations and continuation as its predecessor, most of the code has been rewritten. Compared to FPC, which has good performance on large-scale problems with highly sparse solutions, FPC AS works better overall and much better on certain difficult problems arising in compressed sensing, to name a few, those with sparse, but not highly sparse, solutions and those whose solutions have both very large and very small nonzero components (i.e., the solutions have huge dynamic ranges). In the solutions of these problems, there are certain nonzero components difficult to identify because they are either too small or have only slight advantage to represent b over some of the others. FPC AS was designed with active set identification and sub-optimization to help recover these components in the solutions.