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@inproceedings{54266,
author = {Bartl, David},
address = {Ostrava},
booktitle = {Proceedings of the 14th International Conference on Strategic Management and its Support by Information Systems 2021},
keywords = {theorems of the alternative; systems of linear inequalities; Farkas’ Lemma; linearly ordered vector spaces; linearly ordered fields},
howpublished = {elektronická verze "online"},
language = {eng},
location = {Ostrava},
isbn = {978-80-248-4521-0},
pages = {25-32},
publisher = {VŠB – Technical University of Ostrava, Faculty of Economics},
title = {A universal theorem of the alternative},
url = {https://drive.google.com/file/d/1wV66Mqrrm_uJPpFqmyREvHX0NqUHo8aO/view},
year = {2021}
}
TY - JOUR
ID - 54266
AU - Bartl, David
PY - 2021
TI - A universal theorem of the alternative
PB - VŠB – Technical University of Ostrava, Faculty of Economics
CY - Ostrava
SN - 9788024845210
KW - theorems of the alternative
KW - systems of linear inequalities
KW - Farkas’ Lemma
KW - linearly ordered vector spaces
KW - linearly ordered fields
UR - https://drive.google.com/file/d/1wV66Mqrrm_uJPpFqmyREvHX0NqUHo8aO/view
N2 - 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.
ER -
BARTL, David. A universal theorem of the alternative. Online. In \textit{Proceedings of the 14th International Conference on Strategic Management and its Support by Information Systems 2021}. Ostrava: VŠB – Technical University of Ostrava, Faculty of Economics, 2021, s.~25-32. ISBN~978-80-248-4521-0.
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