This technique note aims at distributed design for nuclear norm (the sum of all singular values) minimization with linear operator equality constraints over a multi-agent network. The problem is reformulated as a standard distributed structure by introducing substitutional variables. Based on projected primal-dual method and derivative feedback techniques, a distributed continuous-time algorithm for each agent is proposed. It is shown that the algorithm can converge to an optimal solution for any initial condition and the average convergence rate is O(1/t). Numerical examples about three classical problems: linear matrix equality constraints, cardinality minimization and matrix completion, are provided for illustration.

中文翻译：

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带约束的线性矩阵方程核范数最小化的分布式设计


本技术说明旨在针对多智能体网络上的线性算子等式约束进行核范数（所有奇异值的总和）最小化的分布式设计。通过引入替代变量，该问题被重新表述为标准分布式结构。基于投影原对偶方法和导数反馈技术，提出了每个智能体的分布式连续时间算法。结果表明，该算法对于任何初始条件都能收敛到最优解，平均收敛速度为O(1/t)。提供了关于三个经典问题的数值示例：线性矩阵等式约束、基数最小化和矩阵完成。