Geodesic
On stability and quasi-stability radii for a~vector combinatorial problem with a~parametric optimality principle
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2009), pp. 55-61.

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A vector combinatorial linear problem with a parametric optimality principle that allows us to relate the well-known choice functions of jointly-extremal and Pareto solution is considered. A quantitative analysis of stability for the set of generalized efficient trajectories under the independent perturbations of coefficients of linear functions is performed. Formulas of stability and quasi-stability radii are obtained in the $l_\infty$-metric. Some results published earlier are derived as corollaries. 
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Vladimir A. Emelichev; Evgeny E. Gurevsky; Andrey A. Platonov. On stability and quasi-stability radii for a~vector combinatorial problem with a~parametric optimality principle. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2009), pp. 55-61. http://geodesic.mathdoc.fr/item/BASM_2009_2_a3/

[1] Pareto V., Manuel d'économie politique, Giard, Paris, 1909

[2] Sholomov L. A., Logical methods for investigating of discrete models of choice, Nauka, Moskow, 1989 (in Russian) | MR | Zbl

[3] Yudin D. B., Computational methods of desicion making theory, Nauka, Moskow, 1989 (in Russian) | MR | Zbl

[4] Leontev V. K., “Stability of linear discrete problems”, Cybernetics Problems, 35, 1979, 169–184 (in Russian) | MR | Zbl

[5] Emelichev V. A., Kravtsov M. K., “Stability in vector optimization path problems”, Cybernetics and Systems Analysis, 31:4 (1995), 599–604 | DOI | MR | Zbl

[6] Gordeev E. N., Leontev V. K., “General approach of stability solution investigating of discrete optimization problems”, Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki, 36:1 (1996), 66–72 (in Russian) | MR | Zbl

[7] Emelichev V. A., Girlich E., Nikulin Yu. V., Podkopaev D. P., “Stability and regularization of vector problems of integer linear programming”, Optimization, 51:4 (2002), 645–676 | DOI | MR | Zbl

[8] Bukhtoyarov S. E., Emelichev V. A., “Optimality principle parametrization (from Pareto to Slater) and stability of multicriteria trajectory problems”, Diskretnyi Analiz i Issledovanie Operatsii Seriya 2, 10:2 (2003), 3–18 (in Russian) | MR

[9] Bukhtoyarov S. E., Emelichev V. A., “Measure of stability for a finite cooperative game with a parametric optimality principle (from Pareto to Nash)”, Computational Mathematics and Mathematical Physics, 46:7 (2006), 1193–1199 | DOI | MR

[10] Emelichev V. A., Gurevsky E. E., Platonov A. A., “Measure of stability for a finite cooperative game with a generalized concept of equilibrium”, Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2006, no. 3(52), 17–26 | MR | Zbl

[11] Podinovskii V. V., Nogin V. D., Pareto-optimal solutions of multiobjective problems, Nauka, Moscow, 1982 (in Russian)

[12] Bukhtoyarov S. E., Emelichev V. A., “Stability measure of a vector linear trajectory problem with jointly-extremal optimality principle”, Vestnik BGU Seriya 1, 2002, no. 3, 84–86 (in Russian) | MR

[13] Emelichev V. A., Kravtsov M. K., Podkopaev D. P., “On the quasistability of trajectory problems of vector optimization”, Mathematical Notes, 63:1 (1998), 19–24 | DOI | MR | Zbl

[14] Emelichev V. A., Kuzmin K. G., “Quasi-stability measure of a vector combinatorial problem with a parametric optimality principle in the $l_1$-metric”, Izvestiya Vuzov. Matematika, 2005, no. 12, 3–10 (in Russian) | MR

[15] Bukhtoyarov S. E., Emelichev V. A., Stepanishina Yu. V., “Stability of discrete vector problems with the parametric principle of optimality”, Cybernetics and Systems Analysis, 39:4 (2003), 604–614 | DOI | MR | Zbl

[16] Emelichev V. A., Kuzmin K. G., “Finite cooperative games with a parametric concept of equilibrium under uncertainty conditions”, Journal of Computer and Systems Sciences International, 45:2 (2006), 276–281 | DOI | MR | Zbl