Distributed Signal Processing and Optimization Based on In-Network Subspace Projections

We study distributed optimization and processing of subspace-constrained signals in multi-agent networks with sparse connectivity. We introduce the first optimization framework based on distributed subspace projections, aimed at minimizing a network cost function depending on the specific processing task, while imposing subspace constraints on the final solution. The proposed method hinges on (sub)gradient optimization techniques while leveraging distributed projections as a mechanism to enforce subspace constraints in a cooperative and distributed fashion. Asymptotic convergence rates to optimal solutions of the problem are established under different assumptions (e.g., nondifferentiability, nonconvexity, etc.) on the objective function. We also introduce an extension of the framework that works with constant step-sizes, thus enabling faster convergence to optimal solutions of the optimization problem. Our algorithmic framework is very flexible and can be customized to a variety of problems in distributed signal processing. Finally, numerical tests on synthetic and realistic data illustrate how the proposed methods compare favorably to existing distributed algorithms.