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 Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, Number 2, Pages 58–67 (Mi basm19)

Research articles

Measure of quasistability of a vector integer linear programming problem with generalized principle of optimality in the Helder metric

Vladimir A. Emelichev, Andrey A. Platonov

Belarussian State University, Minsk, Belarus

Abstract: A vector integer linear programming problem is considered, principle of optimality of which is defined by a partitioning of partial criteria into groups with Pareto preference relation within each group and the lexicographic preference relation between them. Quasistability of the problem is investigated. This type of stability is a discrete analog of Hausdorff lower semicontinuity of the many-valued mapping that defines the choice function. A formula of quasistability radius is derived for the case of metric $l_p$, $1\leq p\leq\infty$ defined in the space of parameters of the vector criterion. Similar formulae had been obtained before only for combinatorial (boolean) problems with various kinds of parametrization of the principles of optimality in the cases of $l_1$ and $l_{\infty}$ metrics [1–4], and for some game theory problems [5–7].

Keywords and phrases: Vector integer linear programming problem, Pareto set, lexicographic order, generalized effective solution, quasistability radius, Helder metric.

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MSC: 90C10, 90C29, 90C31
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Citation: Vladimir A. Emelichev, Andrey A. Platonov, “Measure of quasistability of a vector integer linear programming problem with generalized principle of optimality in the Helder metric”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, no. 2, 58–67

Citation in format AMSBIB
\Bibitem{EmePla08} \by Vladimir~A.~Emelichev, Andrey~A.~Platonov \paper Measure of quasistability of a~vector integer linear programming problem with generalized principle of optimality in the Helder metric \jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat. \yr 2008 \issue 2 \pages 58--67 \mathnet{http://mi.mathnet.ru/basm19} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2435801} \zmath{https://zbmath.org/?q=an:1214.90087} 

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

This publication is cited in the following articles:
1. Vladimir Emelichev, Eberhard Girlich, Olga Karelkina, “Postoptimal analysis of multicriteria combinatorial center location problem”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2009, no. 3, 13–29
2. Emelichev V., Nikulin Yu., “On the Quasistability Radius For a Multicriteria Integer Linear Programming Problem of Finding Extremum Solutions”, Cybern. Syst. Anal., 55:6 (2019), 949–957
3. Vladimir A. Emelichev, Sergey E. Bukhtoyarov, “On two stability types for a multicriteria integer linear programming problem”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 1, 17–30
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