Consensus-based distributed algorithm for GEP

The generalized eigenvalue problem (GEP) plays a significant role in signal processing and machine learning. This paper proposes a consensus-based distributed algorithm for GEP in multi-agent systems, where the data are distributively stored across agents. The distributed GEP is reformulated as a consensus optimization, but the presence of its quadratic inseparable constraint makes the considered problem more challenging. To deal with it, a sequential method combined with the alternating direction method of multipliers is proposed, which requires communication between multiple pairs of nodes. Theoretical analysis shows the proposed algorithm will converge to the set of stationary solutions. And the numerical experiments on synthetic and real-world datasets validate that the approximated solution is competitive to the centered results.