Abstract
A system of linear constraints is investigated. The system describes the domain of feasible solutions of a linear optimization problem to which a linear-fractional optimization problem on arrangements is reduced. A system of nonreducible constraints of a polyhedrom is established for the linear-fractional optimization problem on arrangements.
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REFERENCES
I. V. Sergienko and M. F. Kaspshitskaya, Models and Methods of Solution of Combinatorial Optimization Problems on Computers [in Russian], Naukova Dumka, Kiev (1981).
N. Z. Shor and D. I. Solomon, Decompositional Methods in Fractional Programming [in Russian], Shtiintsa, Kishinev (1989).
V. A. Emelichev, M. M. Kovalev, and M. K. Kravtsov, Polyhedrons, Graphs, and Optimization [in Russian], Nauka, Moscow (1981).
Yu. G. Stoyan and S. V. Yakovlev, Mathematical Models and Optimization Methods of Geometric Design [in Russian], Naukova Dumka, Kiev (1986).
Yu. G. Stoyan, “A Map** of Combinatorial Sets into an Euclidean Space,” Prepr. Inst. Probl. Mashinostr. AN UkrSSR, Kharkov (1982).
O. A. Yemets, Euclidean Combinatorial Sets and Optimization on Them: Innovations in Mathematical Programming (An Educational Book) [in Russian], UMK VO, Kiev (1992).
Yu. G. Stoyan and O. O. Yemets, Theory and methods of Euclidean Combinatorial Optimization [in Ukrainian], Inst. Systemn. Doslidhz. Osvity, Kyiv (1993).
Yu. G. Stoyan, S. V. Yakovlev, O. A. Yemets, and O. A. Valuiskaya, “Construction of convex continuations for functions defined on a hypersphere,” Kibern. Sist. Anal., No. 2, 27–37 (1998).
O. A. Yemets, “Extremal properties of nondifferentiable convex functions on an Euclidean set of combinations with recurrences,” Ukr. Mat. Zh., 46, No.6, 680–691 (1994).
O. A. Yemets and A. A. Roskladka, “Algorithmic solution of two parametric optimization problems on a set of complete combinations,” Kibern. Sist. Anal., No. 6, 160–165 (1999).
O. O. Yemets and S. I. Nedobachii, “A general permutable polyhedron: A nonreducible system of linear constraints and equations of all its hyperfaces,” Naukovi Visti NTUU “KPI,” No. 1, 100–106 (1998).
O. O. Yemets and L. M. Kolechkina, “Optimization problems on permutations with homographic objective functions: Properties of sets of feasible solutions,” Ukr. Mat. Zh., 52, No.12, 1630–1640 (2000).
O. O. Yemets, L. M. Kolechkina, and S. I. Nedobachii, “Investigation of domains of Euclidean combinatorial optimization problems on permutable sets,” Yu. Kondratyuk Techn. Univ., ChPKP “Legat,” Poltava (1999).
O. A. Yemets, L. A. Yevseeva, and N. G. Romanova, “A Mathematical Interval Model of a Combinatorial Problem of Packing of Color Rectangles,” Kibern. Sist. Anal., No. 3, 131–138 (2001).
O. O. Yemets, S. I. Nedobachii, and L. M. Kolechkina, “A nonreducible system of constraints of a combinatorial polyhedron in a linear-fractional optimization problem on permutations,” Discret. Mat., 13, No.1, 110–118 (2001).
O. O. Yemets, O. V. Roskladka, and S. I. Nedobachii, “A nonreducible system of constraints for a general polyhedron of arrangements,” Ukr. Mat. Zh., 55, No.1, 3–11 (2003).
O. A. Yemets and E. V. Roskladka, “Solution of a Euclidean combinatorial optimization problem by the dynamic programming method,” Kibern. Sist. Anal., No. 1, 138–146 (2002).
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Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 107–116, March–April 2005.
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Yemets, O.A., Chernenko, O.A. A Nonreducible System of Constraints of a Combinatorial Polyhedron in a Linear-Fractional Optimization Problem on Arrangements. Cybern Syst Anal 41, 246–254 (2005). https://doi.org/10.1007/s10559-005-0057-0
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DOI: https://doi.org/10.1007/s10559-005-0057-0