Asynchronous primal updates in dual subgradient methods via approximate lagrange multipliers

In this paper, we show that it is possible to make asynchronous primal updates in dual subgradient methods by the use of approximate Lagrange multipliers or Lagrange multipliers with `errors'. An important difference with previous works is that we allow agents to select the Lagrange multiplier they prefer when computing a primal variable or partial subgradient. That is, agents are not constrained to use the `freshest' dual variable available in the system. This allows us not only to obtain asynchronous primal updates, but also to have flexibility as to how to select control actions and therefore model problems. We illustrate the results with a networking example where agents make asynchronous packet transmissions.