The Assignment Problem and Gradient Flows on the Orthogonal Group (NOT KNOWN IF TALK GIVEN BECAUSE AUTHOR HAS LEFT AT&T)

In this paper, we construct a potential function on the special orthogonal group for the Assignment Problem, a common combinatorial optimization problem. We investigate the gradient flow generated by the potential function and show that there is a connection between the non-degenerate local minima and the 2- opt solutions. Our work reinforces the close connection between continuous and combinatorial optimization and may provide a quick analog computational method to construct locally optimal solutions to the problem.