Distributed constraint-coupled optimization via primal decomposition over random time-varying graphs

The paper addresses large-scale, convex optimization problems that need to be solved in a distributed way by agents communicating according random time-varying graph. Specifically, the goal of network is minimize sum local costs, while satisfying and coupling constraints. Agents communicate model which edges an underlying connected graph are active at each iteration with certain non-uniform probabilities. By relying on primal decomposition scheme applied equivalent problem reformulation, we propose novel algorithm negotiate allocation total resource only neighbors communication links. studied as subgradient method block-wise updates, blocks correspond iteration. Thanks this analysis approach, show almost sure convergence optimal cost original asymptotic recovery without resorting averaging mechanisms typically employed dual schemes. Explicit sublinear rates provided under assumption diminishing constant step-sizes. Finally, extensive numerical study plug-in electric vehicle charging corroborates theoretical results.