Quadratic assignment problems with additively monotone matrices and incomplete anti-Monge matrices: conditions for effective solvability

For classes of additively monotone matrices and incomplete anti-Monge matrices, we describe conditions which guarantee the attainment of the optimum of the functional of the quadratic assignment problem at a given permutation. The suggested conditions generalise and unify all special cases of the quadratic assignment problems with anti-Monge and Toeplitz matrices, including the well-known theorem on a permutation of three systems proved by G. H. Hardy, J. E. Littlewood, and G. Pólya in 1926, and all known extensions of this theorem.