Subgradient averaging for multi-agent optimisation with different constraint sets

We consider a multi-agent setting with agents exchanging information over possibly time-varying network, aiming at minimising separable objective function subject to constraints. To achieve this we propose novel subgradient averaging algorithm that allows for non-differentiable functions and different constraint sets per agent. Allowing constraints agent simultaneously communication network constitutes distinctive feature of our approach, extending existing results on distributed methods. highlight the necessity dealing set within optimisation context, analyse problem instance where an does not exhibit convergent behaviour if adapted account sets. For proposed iterative scheme show asymptotic convergence iterates minimum underlying step sizes form ηk+1, η>0. also under size choice η>0, establish rate O(lnkk) in value. demonstrate efficacy method, investigate robust regression ℓ2 regularisation.