Distributed Subgradient Projection Algorithm for Convex Optimization

Abstract—We consider constrained minimization of a sum of convex functions over a convex and compact set, when each component function is known only to a specific agent in a time-varying peer to peer network. We study an iterative optimization algorithm in which each agent obtains a weighted average of its own iterate with the iterates of its neighbors, updates the average using the subgradient of its local function and then projects onto the constraint set to generate the new iterate. We obtain error bounds on the limit of the function value when a constant stepsize is used. Index Terms—distributed optimization, time-varying network, subgradient algorithm