D 2021

A universal theorem of the alternative

BARTL, David

Basic information

Original name

A universal theorem of the alternative

Authors

BARTL, David (203 Czech Republic, guarantor, belonging to the institution)

Edition

Ostrava, Proceedings of the 14th International Conference on Strategic Management and its Support by Information Systems 2021, p. 25-32, 8 pp. 2021

Publisher

VŠB – Technical University of Ostrava, Faculty of Economics

Other information

Language

English

Type of outcome

Stať ve sborníku

Country of publisher

Czech Republic

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

RIV identification code

RIV/47813059:19520/21:A0000187

Organization

Obchodně podnikatelská fakulta v Karviné – Slezská univerzita v Opavě – Repository

ISBN

978-80-248-4521-0

ISSN

Keywords in English

theorems of the alternative; systems of linear inequalities; Farkas’ Lemma; linearly ordered vector spaces; linearly ordered fields

Links

GA21-03085S, research and development project.
Změněno: 3/12/2023 03:37, Bc. Ivana Glabazňová

Abstract

V originále

We present a particular theorem of the alternative for finite systems of linear inequalities. The theorem is universal in the sense that other clas-sical theorems of the alternative (Motzkin’s Theorem and Tucker’s The-orem) are implicit in it; the theorem itself is an extension of Farkas’ Lemma. The presented result also generalizes and unifies both Dax’s new theorem the alternative [Dax, A. (1993). Annals of Operations Re-search, 46, 11–60] and Rohn’s residual existence theorem for linear equations [Rohn, J. (2010). Optimization Letters, 4, 287–292]. The universal theorem of the alternative is established by using Farkas’ Lemma in the setting of a vector space over a linearly ordered (commu-tative or skew) field.

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