A New Proof of the Kuhn–Tucker and Farkas Theorems


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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.

作者简介

Yu. Evtushenko

Dorodnitsyn Computing Centre, Federal Research Center “Computer Science and Control,”
Russian Academy of Sciences

编辑信件的主要联系方式.
Email: evt@ccas.ru
俄罗斯联邦, 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

编辑信件的主要联系方式.
Email: tret@ap.siedlce.pl
俄罗斯联邦, Moscow, 119333; Warsaw, 01-447; Siedlce, 08-110

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