A universal theorem of the alternative

@inproceedings{51622,
   author = {Bartl, David},
   address = {Ostrava},
   booktitle = {Proceedings of the 14th International Conference on Strategic Management and its Support by Information Systems 2021},
   editor = {NĚMEC, R., CHYTILOVÁ, L.},
   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  - 51622
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 NĚMEC, R., CHYTILOVÁ, L. \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, p.~25-32. ISBN~978-80-248-4521-0.