Convergence and Applications of a Gossip-Based Gauss-Newton Algorithm

The Gauss-Newton algorithm is a popular and efficient centralized method for solving non-linear least squares (NLLS) problems. In this paper, a multi-agent distributed version of this algorithm is proposed to solve general NLLS problems in a network, named Gossip-based Gauss-Newton (GGN) algorithm. Furthermore, we analyze and present sufficient conditions for its convergence and show numerically that the GGN algorithm achieves performance comparable to the centralized algorithm, with graceful degradation in case of network failures. More importantly, the GGN algorithm provides significant performance gains compared to other distributed first order methods.