Solving the Lagrangian dual problem for some traffic coordination problems through linear programming

In a series of recent publications, we have addressed a class of traffic coordination problems that can be formulated as combinatorial scheduling problems, and we have developed a Lagrangian duality approach for obtaining (i) strong lower bounds for the corresponding optimal solution, and (ii) potential “seeds” for the construction of feasible, near-optimal solutions to these problems. In those past works, the corresponding “dual” problem was solved through a customized dual-ascent algorithm that took advantage of a distributed representation of the sub-differentials of the underlying “dual” function in order to compute efficiently ascending directions during the optimization process. In this paper we show that the fundamental insights that led to the aforementioned past developments, can also enable an efficient linear programming formulation for the considered “dual” problem. 1