This paper aims at the distributed computation for semi-definite programming (SDP) problems over multi-agent networks. Two SDP problems, including a non-sparse case and a sparse case, are transformed into distributed optimization problems, respectively, by fully exploiting their structures and introducing consensus constraints. Inspired by primal–dual and consensus methods, we propose two distributed algorithms for the two cases with the help of projection and derivative feedback techniques. Furthermore, we prove that the algorithms converge to their optimal solutions, and moreover, their convergences rates are evaluated by the duality gap.

中文翻译：

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用于半定规划的分布式基于共识的求解器：优化观点

本文针对多代理网络上半定规划（SDP）问题的分布式计算。通过充分利用它们的结构并引入共识约束，将两个 SDP 问题，包括非稀疏情况和稀疏情况，分别转化为分布式优化问题。受原始对偶和共识方法的启发，我们在投影和导数反馈技术的帮助下为这两种情况提出了两种分布式算法。此外，我们证明了算法收敛到它们的最优解，此外，它们的收敛率由对偶间隙评估。