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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 7, Pages 1084–1088 (Mi zvmmf10745)  

A new proof of the Kuhn–Tucker and Farkas theorems

Yu. G. Evtushenkoa, A. A. Tret'yakovbac

a Dorodnitsyn Computing Centre, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia
b System Research Institute, Polish Academy of Sciences, Warsaw, Poland
c Faculty of Sciences, Siedlce University, Siedlce, Poland

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.

Key words: projection, Kuhn–Tucker theorem, convex hull, optimality conditions, local minimum.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 27


DOI: https://doi.org/10.31857/S004446690000372-0

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:7, 1035–1039

Bibliographic databases:

UDC: 519.85
Received: 11.05.2017
Revised: 01.11.2017

Citation: Yu. G. Evtushenko, A. A. Tret'yakov, “A new proof of the Kuhn–Tucker and Farkas theorems”, Zh. Vychisl. Mat. Mat. Fiz., 58:7 (2018), 1084–1088; Comput. Math. Math. Phys., 58:7 (2018), 1035–1039

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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