On distributed optimization under inequality and equality constraints via penalty primal-dual methods

We consider a multi-agent convex optimization problem where the agents are to minimize a sum of local objective functions subject to a global inequality constraint, a global equality constraint and a global constraint set. We devise a distributed primal-dual subgradient algorithm which is based on the characterization of the primal-dual optimal solutions as the saddle points of the penalty function. This algorithm allows the agents exchange information over networks with time-varying topologies and asymptotically agree on an optimal solution and the optimal value.