Další formáty:
BibTeX
LaTeX
RIS
@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.
|