LAUSR

We consider a class of generalized DC (difference-of-convex functions) programming, which refers to the problem of minimizing the sum of two convex (possibly nonsmooth) functions minus one smooth convex part. To efficiently exploit the structure of the problem under consideration, in this paper, we shall introduce a unified Douglas–Rachford method in Hilbert space. As an interesting byproduct of the unified framework, we can easily show that our proposed algorithm is able to deal with convex composite optimization models. Due to the nonconvexity of DC programming, we prove that the proposed method is convergent to a critical point of the problem under some assumptions. Finally, we demonstrate numerically that our proposed algorithm performs better than the state-of-the-art DC algorithm and alternating direction method of multipliers (ADMM) for DC regularized sparse recovery problems.