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Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 4, Pages 43–52 (Mi timm1352)  

This article is cited in 1 scientific paper (total in 1 paper)

The set of target vectors in a problem of semi-infinite linear programming with a duality gap

N. N. Astaf'eva, A. V. Ivanovb, S. P. Trofimovb

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: We propose a geometric method for the analysis of duality relations in a pair of semi-infinite linear programming (SILP) problems. The method is based on the use of the conical hull of the coefficients in the constraint system. A relation between the presence of a duality gap and the nonclosedness of the boundary of the conical hull of points in a multidimensional space is established. The geometric approach is used to construct an opposite pair of dual problems and to explore the duality relation for this pair. We construct a nontrivial example of a SILP problem in which the duality gap occurs for noncollinear target vectors.

Keywords: semi-infinite linear programming, duality gap, geometric approach, convex nonclosed cone, set of target vectors.

Funding Agency Grant Number
Russian Science Foundation 14-11-00109


DOI: https://doi.org/10.21538/0134-4889-2016-22-4-43-52

Full text: PDF file (191 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2019, 304, suppl. 1, S14–S22

Bibliographic databases:

UDC: 519.852.2
MSC: 90C34
Received: 20.06.2016

Citation: N. N. Astaf'ev, A. V. Ivanov, S. P. Trofimov, “The set of target vectors in a problem of semi-infinite linear programming with a duality gap”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 4, 2016, 43–52; Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S14–S22

Citation in format AMSBIB
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\by N.~N.~Astaf'ev, A.~V.~Ivanov, S.~P.~Trofimov
\paper The set of target vectors in a problem of semi-infinite linear programming with a duality gap
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2016
\vol 22
\issue 4
\pages 43--52
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\crossref{https://doi.org/10.21538/0134-4889-2016-22-4-43-52}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3590920}
\elib{http://elibrary.ru/item.asp?id=27350115}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2019
\vol 304
\issue , suppl. 1
\pages S14--S22
\crossref{https://doi.org/10.1134/S0081543819020032}
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    This publication is cited in the following articles:
    1. M. A. Goberna, M. A. Lopez, “Recent contributions to linear semi-infinite optimization: an update”, Ann. Oper. Res., 271:1 (2018), 237–278  crossref  mathscinet  zmath  isi  scopus
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