Alternating direction methods of multipliers (ADMM) have been well studied and effectively used in various application fields. The classical ADMM must solve two subproblems exactly at each iteration. To overcome the difficulty of computing the exact solution of the subproblems, some proximal terms are added to the subproblems. Recently, {{a special proximal ADMM has been studied}} whose regularized matrix in the proximal term is generated by the BFGS update (or limited memory BFGS) at every iteration for a structured quadratic optimization problem. {{The numerical experiments also showed}} that the numbers of iterations were almost same as those by the exact ADMM. In this paper, we propose such a proximal ADMM for more general convex optimization problems, and extend the proximal term by the Broyden family update. We also show the convergence of the proposed method under standard assumptions.

中文翻译：

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用于凸优化问题的具有 Broyden 族的近端 ADMM

乘法器的交替方向方法 (ADMM) 已被很好地研究并有效地用于各种应用领域。经典 ADMM 必须在每次迭代中准确地解决两个子问题。为了克服计算子问题精确解的困难，在子问题中加入了一些最接近的项。最近，{{一种特殊的近端 ADMM 已被研究}}，其近端项中的正则化矩阵由结构化二次优化问题的每次迭代中的 BFGS 更新（或有限内存 BFGS）生成。{{数值实验也表明}}迭代次数与精确ADMM的迭代次数几乎相同。在本文中，我们为更一般的凸优化问题提出了这样的近端 ADMM，并通过 Broyden 族更新扩展了近端项。