Email this article A New Proof of the Kuhn–Tucker and Farkas Theorems
- Authors: Evtushenko Y.G.1, Tret’yakov A.A.1,2,3
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Affiliations:
- 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
- Issue: Vol 58, No 7 (2018)
- Pages: 1035-1039
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/179690
- DOI: https://doi.org/10.1134/S0965542518070072
- ID: 179690
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Abstract
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.
About the authors
Yu. G. Evtushenko
Dorodnitsyn Computing Centre, Federal Research Center “Computer Science and Control,”Russian Academy of Sciences
Author for correspondence.
Email: evt@ccas.ru
Russian Federation, Moscow, 119333
A. 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
Author for correspondence.
Email: tret@ap.siedlce.pl
Russian Federation, Moscow, 119333; Warsaw, 01-447; Siedlce, 08-110
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