A new proof of the Kuhn-Tucker and Farkas theorems
type: Item
instance of: scholarly article
title: A new proof of the Kuhn-Tucker and Farkas theorems
zbMATH Open document ID: 1408.46069
DOI: 10.1134/S0965542518070072
published in: Computational Mathematics and Mathematical Physics
publication date: 2018-10-30T00:00:00Z
review text: The authors present a very simple proof of the Kuhn-Tucker theorem (in the Fritz John form) by using only the well-known formula for calculating the projection of a vector onto a closed, convex set. The proof is given first in the Euclidean setting, and then generalized to Banach spaces. Their approach is also employed to prove Farkas' lemma.
Mathematics Subject Classification ID: 46N10
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 6968558
zbMATH Keywords: projection
zbMATH Keywords: Kuhn-Tucker theorem
zbMATH Keywords: convex hull
zbMATH Keywords: optimality conditions
zbMATH Keywords: local minimum
zbMATH Keywords: Farkas' lemma
author: Yu. G. Evtushenko
author: A. Tret'yakov
reviewed by: Rita Pini
MaRDI profile type: Publication
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full work available at URL: s0965542518070072
OpenAlex ID: W2888380322
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description: scientific article; zbMATH DE number 6968558