V. A. Emelichev, M. K. Kravtsov, D. P. Podkopaev, “On the quasistability of trajectory problems of vector optimization”, Mat. Zametki, 63:1 (1998), 21–27; Math. Notes, 63:1 (1998), 19

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Matematicheskie Zametki, 1998, Volume 63, Issue 1, Pages 21–27
DOI: https://doi.org/10.4213/mzm1244 (Mi mzm1244)

This article is cited in 19 scientific papers (total in 19 papers)

On the quasistability of trajectory problems of vector optimization

V. A. Emelichev, M. K. Kravtsov, D. P. Podkopaev

Belarusian State University

Full-text PDF (208 kB) Citations (19)

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DOI: https://doi.org/10.4213/mzm1244

Abstract: We consider quasistable multicriteria problems of discrete optimization on systems of subsets (trajectory problems). We single out the class of problems for which new Pareto optima can appear, while other optima for the problems do not disappear when the coefficients of the objective functions are slightly perturbed (in the Chebyshev metric). For the case of linear criteria (MINSUM), we obtain a formula for calculating the quasistability radius of the problem.

Received: 26.08.1994
Revised: 29.07.1997

English version:
Mathematical Notes, 1998, Volume 63, Issue 1, Pages 19–24
DOI: https://doi.org/10.1007/BF02316139

Bibliographic databases:

UDC: 519.10

Language: Russian

Citation: V. A. Emelichev, M. K. Kravtsov, D. P. Podkopaev, “On the quasistability of trajectory problems of vector optimization”, Mat. Zametki, 63:1 (1998), 21–27; Math. Notes, 63:1 (1998), 19–24

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm1244

https://doi.org/10.4213/mzm1244

https://www.mathnet.ru/eng/mzm/v63/i1/p21

This publication is cited in the following 19 articles:

V. A. Emelichev, V. I. Mychkov, “Postoptimalnyi analiz vektornogo varianta odnoi investitsionnoi zadachi”, Tr. In-ta matem., 24:1 (2016), 9–18
V. A. Emelichev, V. V. Korotkov, K. G. Kuzmin, “Postoptimal analysis of a vector minimax combinatorial problem”, Cybern Syst Anal, 47:3 (2011), 415
V. A. Emelichev, A. V. Karpuk, K. G. Kuz'min, “On a measure of quasistability of a certain vector linearly combinatorial Boolean problem”, Russian Math. (Iz. VUZ), 54:5 (2010), 6–14
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”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2009, no. 2, 55–61
V. A. Emelichev, K. G. Kuz'min, “Stability criteria in vector combinatorial bottleneck problems in terms of binary relations”, Cybern Syst Anal, 44:3 (2008), 397
Vladimir A. Emelichev, Andrey A. Platonov, “About one discrete analog of Hausdorff semi-continuity of suitable mapping in a vector combinatorial problem with a parametric principle of optimality ("from Slater to lexicographic")”, J. Numer. Anal. Approx. Theory, 35:2 (2006), 131
V. A. Emelichev, K. G. Kuz'min, “Measure of quasistability in the metric $l_1$ of a vector combinatorial problem with a parametric optimality principle”, Russian Math. (Iz. VUZ), 49:12 (2005), 1–8
Emelichev, V, “Stability analysis of the Pareto optimal solutions for some vector boolean optimization problem”, Optimization, 54:6 (2005), 545
V. A. Emelichev, V. N. Krichko, “A formula for the stability radius of a vector $l_\infty$ -extremal trajectory problem”, Discrete Math. Appl., 14:1 (2004), 33–39
S. E. Bukhtoyarov, V. A. Emelichev, “On the quasistability of a vector trajectory problem with a parametric optimality principle”, Russian Math. (Iz. VUZ), 48:1 (2004), 23–27
V. A. Emelichev, K. G. Kuz'min, A. M. Leonovich, “On a type of stability for a vector combinatorial problem with partial criteria of the form $\Sigma$ -MINMAX and $\Sigma$ -MINMIN”, Russian Math. (Iz. VUZ), 48:12 (2004), 15–25
V. A. Emelichev, K. G. Kuz'min, A. M. Leonovich, “Stability in the combinatorial vector optimization problems”, Autom. Remote Control, 65:2 (2004), 227–240
V. A. Emelichev, Yu. v. Stepanishina, “Quasistability of a Vector Trajectory Majority Optimization Problem”, Math. Notes, 72:1 (2002), 34–42
Emelichev, VA, “Stability and regularization of vector problems of integer linear programming”, Optimization, 51:4 (2002), 645
V. A. Emelichev, V. G. Pokhil'ko, “Analysis of the sensitivity of efficient solutions of a vector problem of minimizing linear forms on a set of permutations”, Discrete Math. Appl., 10:4 (2000), 367–378
V. A. Emelichev, Yu. v. Stepanishina, “Quasistability of a vector nonlinear trajectory problem with the Pareto optimality principle”, Russian Math. (Iz. VUZ), 44:12 (2000), 25–30
Yemelichev, VA, “Stability and quasistability of vector trajectory problem of sequential optimization”, Doklady Akademii Nauk Belarusi, 43:3 (1999), 41
Emelichev, VA, “Stability conditions for the vector path problem in lexicographic discrete optimization”, Cybernetics and Systems Analysis, 34:4 (1998), 596
V. A. Emelichev, D. P. Podkopaev, “On a quantitative measure of stability for a vector problem in integer programming”, Comput. Math. Math. Phys., 38:11 (1998), 1727–1731

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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