Gradient projection Newton pursuit for sparsity constrained optimization

Hard-thresholding-based algorithms have seen various advantages for sparse optimization in controlling the sparsity and allowing fast computation. Recent research shows that when techniques of Newton-type methods are integrated, their numerical performance can be improved surprisingly. This paper develops a gradient projection Newton pursuit algorithm mainly adopts hard-thresholding operator employs only certain conditions satisfied. The proposed is capable converging globally quadratically under standard assumptions. When it comes to compressive sensing problems, imposed assumptions much weaker than those many state-of-the-art algorithms. Moreover, extensive experiments demonstrated its high comparison with other leading solvers.