A consensus problem consists of finding a distributed control strategy that brings the state or output of a group of agents to a common value, a consensus point. In this paper, we propose a negotiation algorithm that computes an optimal consensus point for agents modeled as linear control systems subject to convex input constraints and linear state constraints. By primal decomposition and incremental subgradient methods, it is shown that the algorithm can be implemented such that each agent exchanges only a small amount of information per iteration with its neighbors.