An inertial Bregman-Style Improved ADMM for Nonconvex Multi-block Optimization Problems

In this study, a class of Multi-block non-convex optimization with linearly constrained is addressed. An inertial Bregman-style enhanced alternating direction approach of multipliers is researched for addressing the non-convex optimization. The design of the iterative approaches is inspired by the proximal alternating direction technique of multipliers and its inertial counterpart. Compared to the classic ADMM, our proposed method adopts a convex combination method in the multiplier update step. The global convergence analysis is presented with a more relaxed range of parameters for the suggested technique, assuming that the Kurdyka-Lojasiewicz (KL) criterion is satisfied by the auxiliary function and that the sequence produced by the novel method is confined. Finally, we give numerical results on solving signal recovery to validate the efficacy of the suggested strategy.