Robustness and Convergence Analysis of First-Order Distributed Optimization Algorithms over Subspace Constraints

This paper extends algorithms that solve the distributed consensus problem to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint framework, we analyze the performance of these generalized algorithms in terms of worstcase robustness and convergence rate. The utility of our framework is demonstrated by showing how one of the extended algorithms, originally designed for consensus, is now able to solve a multitask inference problem.