Farkas' Lemma, Gale's Theorem, and Linear Programming: the Infinite Case in an Algebraic Way

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F12%3AA130164B" target="_blank" >RIV/61988987:17310/12:A130164B - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Farkas' Lemma, Gale's Theorem, and Linear Programming: the Infinite Case in an Algebraic Way

Original language description

We study a problem of linear programming in the setting of a vector space over a linearly ordered (possibly skew) field. The dimension of the space may be infinite. The objective function is a linear mapping into another linearly ordered vector space over the same field. In that algebraic setting, we recall known results: Farkas' Lemma, Gale's Theorem of the alternative, and the Duality Theorem for linear programming with finite number of linear constraints. Given that ``semi-infinite'' case, i.e. results for finite systems of linear inequalities in an infinite-dimensional space, we are motivated to consider the infinite case: infinite systems of linear inequalities in an infinite-dimensional space. In the described setting, we formulate an infinite variant of Farkas' Lemma along with an infinite variant of Gale's Theorem of the alternative. Finally, we formulate the problem of an infinite linear programming, its dual problem, and the Duality Theorem for the problems.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BB - Applied statistics, operational research

OECD FORD branch

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Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2012

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Global Journal of Mathematical Sciences (GJMS)

ISSN

2164-3709

e-ISSN

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Volume of the periodical

1

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

6

Pages from-to

18-23

UT code for WoS article

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EID of the result in the Scopus database

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