Distributed Solution of MIQP Problems Arising for Networked Systems with Coupling Constraints

Abstract

This paper introduces a scheme for distributed solution for mixed-integer quadratic programming (MIQP) problems, which stem from, e.g., optimal control problems of networked systems involving hybrid dynamics. The centralized solution of this class of problem is often very complicated due to the NP-hard nature of MIQP, especially when a larger number of subsystems is to be considered. The proposed distributed solution is carried out sequentially by employing different stages, each of which uses one optimality condition formulated for the MIQP problem. These conditions guide the decomposition and the solution process, so that the overall complexity is reduced significantly compared to the centralized solution. Efficiency with respect to computation times and performance is confirmed by a set of numerical examples.