Detailed Information on Publication Record
2021
A universal theorem of the alternative
BARTL, DavidBasic 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
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.