Distributed Semidefinite Programming with Application to Large-scale System Analysis

Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled problem has an inherent tree structure, it is possible to devise an efficient distributed algorithm for solving such problems. The proposed algorithm relies on predictor-corrector primal-dual interior-point methods, where we use a message-passing algorithm to compute the search directions distributedly. Message-passing here is closely related to dynamic programming over trees. This allows us to compute the exact search directions in a finite number of steps. This is because, computing the search directions requires a recursion over the tree structure and hence, terminates after an upward and downward pass through the tree. Furthermore this number can be computed apriori and only depends on the coupling structure of the problem. We use the proposed algorithm for analyzing robustness of large-scale uncertain systems distributedly. We test the performance of this algorithm using numerical examples.