Geodesic
Quadratic assignment problems with additively monotone matrices and incomplete anti-Monge matrices: conditions for effective solvability
Diskretnaya Matematika, Tome 19 (2007) no. 1, pp. 105-132

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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. 
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     author = {V. M. Demidenko},
     title = {Quadratic assignment problems with additively monotone matrices and incomplete {anti-Monge} matrices: conditions for effective solvability},
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V. M. Demidenko. Quadratic assignment problems with additively monotone matrices and incomplete anti-Monge matrices: conditions for effective solvability. Diskretnaya Matematika, Tome 19 (2007) no. 1, pp. 105-132. http://geodesic.mathdoc.fr/item/DM_2007_19_1_a12/