Abstract
We consider optimization of functions on combinatorial sets of permutations and n-arrangements mapped to En (the images of these sets are denoted by A nk and B nk , respectively). Bounds are obtained on the minimum for convex and strongly convex functions on convex sets X⊃A nk and X⊃B nk . A theorem on the sufficient condition for a minimum of a convex function on A nk is proved.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Literature Cited
Yu. G. Stoyan, Some Properties of Special Combinatorial Sets [in Russian], Preprint No. 85, Akad. Nauk UkrSSR, Inst. Probl. Mashinostroeniya Khar'kov (1980).
Yu. G. Stoyan and S. V. Yakovlev, Mathematical Models and Optimization Methods of Geometrical Design [in Russian], Naukova Dumka, Kiev (1986).
V. A. Emelichev, M. M. Kovalev, and M. K. Kravtsov, Polyhedra, Graphs. Optimization [in Russian], Nauka, Moscow (1981).
J. G. Rau, “Minimizing a function of permutations of n integers,” Oper. Res.,19, No. 1, 237–240 (1971).
D. A. Suprunenko, V. S. Aizenshtat, and N. A. Lepeshinskii, “Extremal values of functions on permutation sets,” Abstracts of Papers at lst All-Union Conf. on Operations Research [in Russian], Minsk (1972), pp. 61–67.
D. A. Suprunenko and N. N. Metel'skii, “The assignment problem and minimization of the sum of linear forms on a symmetric group,” Kibernetika, No. 3, 64–68 (1973).
Yu. G. Stoyan and S. V. Yakovlev, “Properties of convex functions on the permutation polyhedron,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 3, 69–72 (1988).
I. V. Sergienko, Mathematical Models and Methods of Discrete Optimization [in Russian], Naukova Dumka, Kiev (1985).
Yu. I. Zhuravlev, “Local algorithms of computing information. I, II,” Kibernetika, No. 1, 12–19 (1965); No. 2, 1–11 (1966).
V. S. Mikhalevich, “Sequential optimization algorithms and their application. I, II,” Kibernetika, No. 1, 45–55; No. 2, 85–89 (1965).
A. A. Korbut, I. Kh. Sigal, and Yu. B. Finkel'shtein, “The branch-and-bound method: a survey of theory, algorithms, programs, and applications,” Math. Operationsforsch., Ser. Optim.,8, No. 2, 253–280 (1977).
Additional information
Translated from Kibernetika, No. 3, pp. 83–87, May–June, 1989.
Rights and permissions
About this article
Cite this article
Yakovlev, S.V. Bounds on the minimum of convex functions on Euclidean combinatorial sets. Cybern Syst Anal 25, 385–391 (1989). https://doi.org/10.1007/BF01069996
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01069996