A proximal DC approach for quadratic assignment problem

In this paper, we show that the quadratic assignment problem (QAP) can be reformulated to an equivalent rank constrained doubly nonnegative (DNN) problem. Under framework of difference convex functions (DC) approach, a semi-proximal DC algorithm is proposed for solving relaxation DNN whose subproblems solved by augmented Lagrangian method. We generated sequence converges stationary point corresponding problem, which feasible under some suitable assumptions. Moreover, numerical experiments demonstrate most QAP instances, approach find global optimal solutions efficiently, and others, able provide good in reasonable time.