Abstract
A Boolean vector minimization problem for a threshold function is considered. A formula is obtained for the limit level of perturbations of partial criteria parameters in l 1 metrics that preserve the strict effectiveness of the solution.
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REFERENCES
I. V. Sergienko, L. N. Kozeratskaya, and T. T. Lebedeva, Stability and Parametric Analysis of Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1995).
L. N. Kozeratskaya, T. T. Lebedeva, and I. V. Sergienko, “Stability analysis of discrete optimization problems,” Kibern. Sist. Analiz, No. 3, 78–93 (1993).
I. V. Sergienko, V. A. Roshchin, and N. V. Semenova, “Some integer programming problems with ambiguous data and their solutions,” Probl. Upravl. Inform., No. 6, 116–123 (1998).
Yu. N. Sotskov, V. K. Leontev, and E. N. Gordeev, “Some concepts of stability analysis in combinatorial optimization,” Discr. Appl. Math., 58, No. 2, 169–190 (1995).
H. J. Greenberg, “An annotated bibliography for post-solution analysis in mixed integer programming and combinatorial optimization,” in: D. L. Woodruff (ed.), Advances in Computational and Stochastic Optimization, Logic Programming and Heuristic Search, Kluwer Acad. Publ., Boston (1998), pp. 97–148.
M. Libura, E. S. van der Poot, G. Sierksma, and J. A. A. van der Veen, “Stability aspects of the traveling salesman problem based on k-best solutions,” Discr. Appl. Math., 87, 159–185 (1998).
V. A. Emelichev, E. Girlich, Yu. V. Nikulin, and D. P. Podkopaev, “Stability and regularization of vector problems of integer linear programming,” Optimization, 51, No. 4, 645–676 (2002).
S. E. Bukhtoyarov, V. A. Emelichev, and Yu. V. Stepanishina, “Stability of discrete vector problems with the parametric principle of optimality,” Kibern. Sist. Analiz, No. 4, 155–166 (2003).
V. A. Emelichev and V. G. Pokhil'ko, “Sensitivity analysis of the solutions of a vector problem of minimizing linear forms on a set of substitutions,” Diskr. Mat., 12, Issue 3, 37–48 (2000).
V. A. Emelichev and Yu. V. Nikulin, “On stability of an effective solution of a vector problem of integer linear programming,” Dokl. NAN Byelarusi, 44, No. 4, 26–28 (2000).
V. A. Emelichev and Yu. V. Stepanishina, “Multicriterial linear combinatorial problems: parametrization of optimality principle and stability of effective solutions,” Diskr. Mat., 13, Issue 4, 43–51 (2001).
V. A. Emelichev and V. N. Krichko, “Stability radius of an effective solution of a quadratic vector problem of Boolean programming,” Zh. Vych. Mat. Mat. Fiz., 41, No. 2, 346–350 (2001).
Yu. A. Zuev, “Threshold functions and threshold representations of Boolean functions,” Mat. Probl. Kibern., Issue 5, 5–61 (1994).
E. N. Gordeev, “Stability analysis of the problem on a shortest skeleton in l 1 metric,” Zh. Vych. Mat. Mat. Fiz., 39, 770–778 (1990).
E.N. Gordeev, “Stability analysis in optimization problems in the metric l 1, ” Kibern. Sist. Analiz, No. 2, 132–144 (2001).
V. K. Leont'ev and K. Kh. Mamutov, “Solution stability in linear Boolean programming problems,” Zh. Vych. Mat. Mat. Fiz., 28, No. 10, 1475–1481 (1988).
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Emelichev, V.A., Kuz'min, K.G. Stability Radius for a Strictly Effective Solution to a Vector Minimization Problem for Threshold Functions in l 1 Metric. Cybernetics and Systems Analysis 40, 358–362 (2004). https://doi.org/10.1023/B:CASA.0000041992.79934.5f
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DOI: https://doi.org/10.1023/B:CASA.0000041992.79934.5f