Interior Point Decomposition for Multi-Agent Optimization ?

In this paper we present the application of the interior-point decomposition (IPD) method, which was originally formulated for stochastic programming, to optimization problems involving multiple agents that are coupled through constraints and objectives. IPD eliminates the need to communicate local constraints and cost functions for all variables that relate to internal dynamics and objectives of the agents. Instead, by using embedded barrier functions, the problem is solved in the space of coupling variables, which are in general much lower in dimension compared to internal variables of individual agents. Therefore, IPD contributes to both problem size reduction as well as data hiding. The method is a distributed version of the primal barrier method, with locally and globally feasible iterations and faster convergence compared to first-order distributed optimization methods. Hence, IPD is suitable for early termination in time-critical applications. We illustrate these attractive properties of the IPD method with a distributed Model Predictive Control (MPC) application in the context of smart-grids, where a collection of commercial buildings provide voltage support to a distribution grid operator.