## A partially symmetric regularized alternating direction method of multipliers for nonconvex multi-block optimization.(Chinese. English summary)Zbl 1513.90142

Summary: The researches on the alternating direction method of multiplier method (ADMM) for solving two-block optimization have been gradually mature and perfect. However, the studies on ADMM for solving nonconvex multi-block optimization are relatively few. In this paper, we first propose a partially symmetric regularized ADMM for nonconvex multi-block optimization with linear constraints. Second, under appropriate assumptions including the region of the two parameters in the updating formulas for the multiplier, the global convergence of the proposed method is proved. Third, when the augmented Lagrangian function satisfies the Kurdyka-Łojasiewicz (KL) property, the strong convergence of the method is proved. Furthermore, when the associated KL property function has a special structure, the sublinear and linear convergence rate of the method are obtained. Finally, some preliminary numerical experiments are carried out, and this shows that the proposed method is numerically effective.

### MSC:

 90C26 Nonconvex programming, global optimization 90C30 Nonlinear programming

BADMM
Full Text:

### References:

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