Convergence and noise effect analysis for generalized gossip-based distributed optimization

The generalized gossip-based subgradient algorithm has been recently proposed for solving distributed optimization problems associated with multi-agent networks. The algorithm provides a generalization such that the optimization process can operate in the entire spectrum of “complete consensus” to “complete disagreement”. Beyond the existing work of first-order convergence analysis results, this paper presents the second-order convergence results and convergence rate estimates for the proposed algorithm. Moreover, this work also takes into consideration the effect of noise in subgradient estimates as well as measurements on the function value error bounds. A numerical case study based on a building energy system is presented to validate the algorithm.