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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 9, Pages 1462–1471 (Mi zvmmf11126)  

A new view of some fundamental results in optimization

Yu. G. Evtushenkoabc, A. A. Tret'yakovade

a Dorodnitsyn Computing Centre, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, 119333 Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, 141700 Russia
c Moscow Aviation Institute (National Research University), Moscow, 125080 Russia
d Siedlce University of Natural Sciences and Humanities
e System Research Institute, Polish Academy of Sciences, Warsaw, 01-447 Poland

Abstract: Some fundamental optimization results are proved in new ways, which are not traditional and provide a new view of well-known results. Constructions of $p$-regularity theory are used to justify the facts under consideration, and the 2-factor method is applied to solve singular problems.

Key words: optimization, singularity, Kuhn–Tucker theorem, Farkas' lemma, cone closedness, 2-factor method, 2-regularity

DOI: https://doi.org/10.31857/S0044466920090082


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:9, 1412–1421

Bibliographic databases:

UDC: 519.855
Received: 18.07.2019
Revised: 31.08.2019
Accepted:09.04.2020

Citation: Yu. G. Evtushenko, A. A. Tret'yakov, “A new view of some fundamental results in optimization”, Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020), 1462–1471; Comput. Math. Math. Phys., 60:9 (2020), 1412–1421

Citation in format AMSBIB
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\paper A new view of some fundamental results in optimization
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 9
\pages 1462--1471
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\crossref{https://doi.org/10.31857/S0044466920090082}
\elib{https://elibrary.ru/item.asp?id=43832506}
\transl
\jour Comput. Math. Math. Phys.
\yr 2020
\vol 60
\issue 9
\pages 1412--1421
\crossref{https://doi.org/10.1134/S0965542520090080}
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