Abstract
We consider the optimization of quadratic functions on the set of permutations in Rn. Extremal properties of these functions are studied. Branch-and-bound methods are proposed for the solution of these optimization problems.
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Literature Cited
V. A. Emelichev, M. M. Kovalev, and M. K. Kravtsov, Polyhedra, Graphs, and Optimization [in Russian], Nauka, Moscow (1981).
Yu. G. Stoyan and S. V. Yakovlev, Mathematical Models and Optimization Methods of Geometical Design [in Russian], Naukova Dumka, Kiev (1986).
A. Brenstetz, An Introduction to the Theory of Convex Polyhedra [Russian translation], Mir, Moscow (1988).
M. M. Kovalev, A. N. Isachenko, and Nguen Ngia, "Linearization of combinatorial optimization problems," Dokl. Akad. Nauk BSSR,22, No. 10, 869–872 (1978).
M. F. Kaspshitskaya, "On local extrema of discrete functions," Dokl. Akad. Nauk UkrSSR, Ser. A, No. 3, 66–69 (1984).
D. A. Suprunenko and N. N. Metel'skii, "Assignment problems and minimization of the sum of linear forms on a symmetric group," Kibernetika, No. 3, 64–68 (1973).
D. A. Suprunenko, V. S. Aizenshtat, and N. A. Lepeshinskii, "Extremal values of functions on permutation sets," Abstracts of papers at 1st All-Union Conf. on Operations Research, Minsk (1972), pp. 61–67.
Yu. G. Stoyan and S. V. Yakovlev, "Properties of convex functions on a permutation polyhedron," Dokl. Akad. Nauk UkrSSR, Ser. A, No. 3, 69–72 (1988).
S. V. Yakovlev, "Bounds on the minimum of convex functions in Euclidean combinatorial spaces," Kibernetika, No. 3, 83–87 (1989).
J. G. Rau, "Minimizing a function of permutations of an integer," Oper. Res.,19, No. 1, 237–240 (1971).
A. A. Bolotnikov, "On the best balancing of a disk with a distribution of peripheral masses," Probl. Mashinostr., No. 6, 68–74 (1978).
V. A. Selyutin, Computer Design of Electronic Devices [in Russian], Sovetskoe Radio, Moscow (1977).
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Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 97–104, July–August, 1991.
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Stoyan, Y.G., Yakovlev, S.V. & Parshin, O.V. Quadratic optimization on combinatorial sets in Rn . Cybern Syst Anal 27, 561–567 (1991). https://doi.org/10.1007/BF01130367
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DOI: https://doi.org/10.1007/BF01130367