Distributed Semidefinite Programming with Application to Large-scale System Analysis

TL;DR

This paper introduces an efficient distributed algorithm for solving coupled semidefinite programs with a tree structure, enabling faster convergence and reduced computational demand in large-scale system analysis.

Contribution

It presents a novel message-passing based distributed algorithm leveraging primal-dual interior-point methods for SDPs with tree structures, improving efficiency over existing methods.

Findings

The algorithm computes exact search directions in finite steps.

Performance tested on large-scale uncertain systems.

Number of steps depends only on problem structure.

Abstract

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. This algorithm can potentially enjoy the same efficiency as centralized solvers that exploit sparsity. 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. Furthermore this number can be computed a priori 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.