Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization

In this paper, we consider a class of constrained nonconvex regularized minimization problems, where the constraints is linearly constrained. It was reported in the literature that nonconvex regularization usually yields a solution with more desirable sparse structural properties beyond convex ones. However, it is not easy to obtain the proximal mapping associated with nonconvex regularization, due to the imposed linearly constraints. In this paper, the optimization problem with linear constraints is solved by the Linearized Alternating Direction Method of Multipliers (LADMM). Moreover, we present a detailed convergence analysis of the LADMM algorithm for solving nonconvex compositely regularized optimization with a large class of nonconvex penalties. Experimental results on several real-world datasets validate the efficacy of the proposed algorithm.