Distributed consensus has appeared as one of the most important and primary problems in the context of distributed computation and it has received renewed interest in the field of sensor networks (due to recent advances in wireless communications), where solving fastest distributed consensus averaging problem over networks with different topologies is one of the primary problems in this issue. ...

We discuss some implications of linear programming for Mather theory [Mt1-2], [M-F] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an n–dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [F1-3], [E-G]. In memory of Professor Jacques–Loui...

1.1 Complementary Slackness: Full and Approximate Recall our canonical linear programs, where x ∈ R, y ∈ R, A ∈ R, b ∈ R, c ∈ R. Primal (P) min cx Ax ≥ b x ≥ 0 Dual (D) max by A y ≤ c y ≥ 0 Also recall that Strong Duality ensures that if both (P) and (D) have finite optima, they are equal. Assume this is the case. Then, for the optima x and y of the primal and dual programs respectively, we hav...

We propose a new algorithm for the solution of the linear minimum cost network flow problem, based on a sequential shortest path augmentation approach. Each shortest path is constructed by means of the recently proposed auction/shortest path algorithm. This approach allows useful information to be passed from one shortest path construction to the next. However, the naive implementation of this ...

The flow-induced deformation of a membrane in a flow with a pressure gradient is studied. The investigation focuses on the deformation of aerodynamically loaded convertible car roofs. A computational methodology is developed with a line-element structural model that incorporates initial slackness of the flexible roof material. The computed flow-structure interaction yields stable solutions, the...

This paper studies the feedback control of a class of complementary-slackness hybrid mechanical systems. Roughly, the systems we study are composed of an uncontrollable part (the “object”) and a controlled one (the “robot”), linked by a unilateral constraint and an impact rule. A systematic and general control design method for this class of systems is proposed. The approach is a nontrivial ext...

A new DEA model has been introduced recently combining the primal and the dual models in order to impose strong complementary slackness conditions. It was claimed that a reference set that contains the maximum number of efficient units can then be determined. The model is very interesting as a theoretical idea. However, not only does the computational burden increase significantly, but it seems...

This paper studies the duality gap in the simple plant location problem, and presents general formulas for the gap when certain complementary slackness conditions are satisfied. We show that the duality gap derived by Erlenkotter [A dual-based procedure for uncapacitated facility location, Operations Research 26 (1978) 992–1009], and which has been widely used in the literature, is a special ca...