Distributed multiuser optimization: Algorithms and error analysis

We consider a class of multiuser optimization problems in which user interactions are seen through congestion cost functions or coupling constraints. Our primary emphasis lies on the convergence and error analysis of distributed algorithms in which users communicate through aggregate user information. Traditional implementations are reliant on strong convexity assumptions, require coordination across users in terms of consistent stepsizes, and often rule out early termination by a group of users. We consider how some of these assumptions can be weakened in the context of projection methods motivated by fixed-point formulations of the problem. Specifically, we focus on (approximate) primal and primal-dual projection algorithms. We analyze the convergence behavior of the methods and provide error bounds in settings with limited coordination across users and regimes where a group of users may prematurely terminate affecting the convergence point.