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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, номер 2, страницы 58–67
(Mi basm19)
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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
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
Аннотация:
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].
Ключевые слова и фразы:
Vector integer linear programming problem, Pareto set, lexicographic order, generalized effective solution, quasistability radius, Helder metric.
Полный текст:
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Список литературы:
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Реферативные базы данных:
MSC: 90C10, 90C29, 90C31 Поступила в редакцию: 12.12.2007
Язык публикации: английский
Образец цитирования:
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
Цитирование в формате AMSBIB
\RBibitem{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}
Образцы ссылок на эту страницу:
http://mi.mathnet.ru/basm19 http://mi.mathnet.ru/rus/basm/y2008/i2/p58
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
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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
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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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