Multi-agent distributed optimization algorithms for partition-based linear programming (LP) problems

The paper addresses the problem of multi-agent distributed solutions for a class of linear programming (LP) problems which include box constraints on the decision variables and inequality constraints. The major difference with existing literature on distributed solution of LP problems is that each agent is expected to compute only a single or few entries of the global minimizer vector, often referred as a partition-based optimization. This class of LP problems isrelevant in different applications such as optimal power transfer in remotely powered battery-less wireless sensor networks, minimum energy LED luminaries control in smart offices, and optimal temperature control in start buildings. Via a suitable approximation of the originalLP problem, we propose three different primal-dual distributed algorithms based on dual gradient ascent, on the methods of multipliers and on the Alternating Direction Methods of Multipliers.We discuss the computational and communication requirements of these methods and we provide numerical comparisons.