A truncated Newton algorithm for nonconvex sparse recovery

Abstract

Some second-order sufficient conditions are established for problems with ℓ1, SCAD and MCP penalties respectively and then an algorithm with active set strategy is proposed for solving ℓ1, SCAD and MCP penalties based on an approximation of the second order sufficient conditions. The active sets are estimated by an identification technique to identify accurately zero components in a neighborhood of a critical point of ℓ1, SCAD and MCP penalties. In the algorithm, a truncated Newton direction is used to update the free variables, while dk=−xk is used to update the active variables. To accelerate the convergence, a nonmonotone line search strategy is used to guarantee global convergence. Numerical results illustrate that the proposed algorithm is competitive with several well-known methods.