A Distributed Method for Linear Programming Problems With Box Constraints and Time-Varying Inequalities

This letter proposes a multi-agent distributed solution for linear programming (LP) problems with time-invariant box constraints on the decision variables and possibly time-varying inequality constraints. This class of LP problems is relevant in different multi-agent smart systems. In the proposed approach, each agent computes only a single or a few of decision variables, while convergence to the optimal solution for the overall problem is guaranteed. Using a strong convexification of the problem combined with the barrier method, we prove that, despite the fact that the inequalities are time-varying, the tracking error remains bounded, and the bound is proportional to the rate of change of parameters. The effectiveness of the proposed scheme is demonstrated through a simulation study on a wireless power transfer network.