论文标题
非convex非conmooth优化的近端线性化ADMM算法的收敛分析
Convergence Analysis of A Proximal Linearized ADMM Algorithm for Nonconvex Nonsmooth Optimization
论文作者
论文摘要
在本文中，我们考虑了一种近端线性化的交替方向方法（PL-ADMM），用于求解线性约束的非convex和可能非平滑优化问题。该算法是通过在原始更新中使用可变度量近端项的推广，并且在乘数更新中进行了过度删除的步骤。我们证明，该方法生成的序列是有限的，其限制点是关键点。在强大的kurdyka- {oljasiewicz}属性下，我们证明该序列的长度因此会收敛，并且我们驱动其收敛速率。
In this paper, we consider a proximal linearized alternating direction method of multipliers (PL-ADMM) for solving linearly constrained nonconvex and possibly nonsmooth optimization problems. The algorithm is generalized by using variable metric proximal terms in the primal updates and an over-relaxation stepsize in the multiplier update. We prove that the sequence generated by this method is bounded and its limit points are critical points. Under the powerful Kurdyka-{Łojasiewicz} properties we prove that the sequence has a finite length thus converges, and we drive its convergence rates.
