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.

我们考虑一类广义 DC（凸函数差）规划，它指的是最小化两个凸（可能是非光滑）函数之和减去一个光滑凸部分的问题。为了有效地利用所考虑问题的结构，在本文中，我们将在 Hilbert 空间中引入统一的 Douglas-Rachford 方法。作为统一框架的一个有趣的副产品，我们可以很容易地证明我们提出的算法能够处理凸复合优化模型。由于 DC 规划的非凸性，我们证明了所提出的方法在某些假设下收敛到问题的临界点。最后，