A New Proof of the Kuhn–Tucker and Farkas Theorems
- Autores: Evtushenko Y.G.1, Tret’yakov A.A.1,2,3
-
Afiliações:
- Dorodnitsyn Computing Centre, Federal Research Center “Computer Science and Control,” Russian Academy of Sciences
- System Research Institute, Polish Academy of Sciences
- Faculty of Sciences, Siedlce University
- Edição: Volume 58, Nº 7 (2018)
- Páginas: 1035-1039
- Seção: Article
- URL: https://journals.rcsi.science/0965-5425/article/view/179690
- DOI: https://doi.org/10.1134/S0965542518070072
- ID: 179690
Citar
Resumo
For the minimization problem for a differentiable function on a set defined by inequality constraints, a simple proof of the Kuhn–Tucker theorem in the Fritz John form is presented. Only an elementary property of the projection of a point onto a convex closed set is used. The approach proposed by the authors is applied to prove Farkas’ theorem. All results are extended to the case of Banach spaces.
Palavras-chave
Sobre autores
Yu. Evtushenko
Dorodnitsyn Computing Centre, Federal Research Center “Computer Science and Control,”Russian Academy of Sciences
Autor responsável pela correspondência
Email: evt@ccas.ru
Rússia, Moscow, 119333
A. Tret’yakov
Dorodnitsyn Computing Centre, Federal Research Center “Computer Science and Control,”Russian Academy of Sciences; System Research Institute, Polish Academy of Sciences; Faculty of Sciences, Siedlce University
Autor responsável pela correspondência
Email: tret@ap.siedlce.pl
Rússia, Moscow, 119333; Warsaw, 01-447; Siedlce, 08-110
Arquivos suplementares
