In this paper, a class of nonconvex optimization with linearly constrained is considered. An inertial Bregman generalized alternating direction method of multiplies is investigated for solving the nonconvex optimization. The iterative schemes are formulated in the spirit of the proximal alternating direction method of multipliers and its inertial variant. The proximal term is introduced via Bregman distance, a fact that allows us to derive new proximal splitting algorithms for large-scale separable optimization problems. Under some assumptions, we prove that the iterative sequence generated by the algorithm converges to a critical point of the considered problem. Finally, we report some preliminary numerical results on solving signal recovery and SCAD penalty problems to verify the efficiency of the proposed method.

在本文中，考虑了一类具有线性约束的非凸优化。研究了求解非凸优化的惯性Bregman广义交替方向乘法方法。迭代方案是根据乘法器的近端交替方向方法及其惯性变体的精神制定的。近端项是通过 Bregman 距离引入的，这一事实使我们能够为大规模可分离优化问题推导出新的近端分裂算法。在一些假设下，我们证明算法生成的迭代序列收敛到所考虑问题的临界点。最后，我们报告了一些关于解决信号恢复和 SCAD 惩罚问题的初步数值结果，以验证所提出方法的有效性。