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.

We consider the uplink power control problem where mobile users in different cells are communicating with their base stations. We formulate the power control problem as the minimization of a sum of convex functions. Each component function depends on the channel coefficients from all the mobile users to a specific base station and is assumed to be known only to that base station (only CSIR). We then view the power control problem as a distributed optimization problem that is to be solved by the base stations and propose convergent, distributed and iterative power control algorithms. These algorithms require each base station to communicate with the base stations in its neighboring cells in each iteration and are hence non-autonomous. Since the base stations are connected through a wired backbone the communication overhead is not an issue. The convergence of the algorithms is shown theoretically and also verified through numerical simulations.