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Mat. Zametki, 1998, Volume 63, Issue 1, Pages 21–27 (Mi mz1244)  

This article is cited in 16 scientific papers (total in 16 papers)

On the quasistability of trajectory problems of vector optimization

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

Belarusian State University

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.


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English version:
Mathematical Notes, 1998, 63:1, 19–24

Bibliographic databases:

UDC: 519.10
Received: 26.08.1994
Revised: 29.07.1997

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
\by V.~A.~Emelichev, M.~K.~Kravtsov, D.~P.~Podkopaev
\paper On the quasistability of trajectory problems of vector optimization
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 1
\pages 21--27
\jour Math. Notes
\yr 1998
\vol 63
\issue 1
\pages 19--24

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    This publication is cited in the following articles:
    1. Emelichev, VA, “Stability conditions for the vector path problem in lexicographic discrete optimization”, Cybernetics and Systems Analysis, 34:4 (1998), 596  crossref  mathscinet  zmath  isi  scopus
    2. 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  mathnet  mathscinet  zmath
    3. Yemelichev, VA, “Stability and quasistability of vector trajectory problem of sequential optimization”, Doklady Akademii Nauk Belarusi, 43:3 (1999), 41  mathscinet  isi
    4. 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  mathnet  crossref  mathscinet  zmath
    5. 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  mathnet  mathscinet  zmath
    6. V. A. Emelichev, Yu. v. Stepanishina, “Quasistability of a Vector Trajectory Majority Optimization Problem”, Math. Notes, 72:1 (2002), 34–42  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Emelichev, VA, “Stability and regularization of vector problems of integer linear programming”, Optimization, 51:4 (2002), 645  crossref  mathscinet  zmath  isi  scopus
    8. 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  mathnet  crossref  crossref  mathscinet  zmath
    9. 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  mathnet  mathscinet  zmath
    10. 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  mathnet  mathscinet
    11. 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  mathnet  crossref  mathscinet  zmath  isi
    12. 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  mathnet  mathscinet
    13. Emelichev, V, “Stability analysis of the Pareto optimal solutions for some vector boolean optimization problem”, Optimization, 54:6 (2005), 545  crossref  mathscinet  zmath  isi  elib  scopus
    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  mathnet  mathscinet  zmath
    15. 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  mathnet  crossref  mathscinet
    16. V. A. Emelichev, V. I. Mychkov, “Postoptimalnyi analiz vektornogo varianta odnoi investitsionnoi zadachi”, Tr. In-ta matem., 24:1 (2016), 9–18  mathnet
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