Distributed Continuous Time Optimization Algorithms over Unbalanced Graphs

This paper investigates two distributed optimization schemes with or without feasible set constraints over unbalanced graphs, respectively. To overcome the inaccuracy convergence problem of unbalanced graphs, we propose two continuous time algorithms with an inexact gradient tracking dynamic. The first one is a distributed optimization algorithm without feasible set constraints and the second one is improved from the first one with feasible set constraints. Moreover, we provide the convergence analyses for the two optimization algorithms.