An Extremum Principle for Smooth Problems

We derive an extremum principle. It can be treated as an intermediate result between the celebrated smooth-convex extremum principle due to Ioffe and Tikhomirov and the Dubovitskii–Milyutin theorem. The proof of this principle is based on a simple generalization of the Fermat’s theorem, the smooth-c...

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Main Authors:	Dariusz Idczak, Stanisław Walczak
Format:	Article
Language:	English
Published:	MDPI AG 2020-11-01
Series:	Games
Subjects:	extremum principle Fermat’s theorem local implicit function theorem
Online Access:	https://www.mdpi.com/2073-4336/11/4/56

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spelling	doaj-a92117832b9d47d2adc25036eaa4f7e02020-11-28T00:00:22ZengMDPI AGGames2073-43362020-11-0111565610.3390/g11040056An Extremum Principle for Smooth ProblemsDariusz Idczak0Stanisław Walczak1Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, PolandFaculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, PolandWe derive an extremum principle. It can be treated as an intermediate result between the celebrated smooth-convex extremum principle due to Ioffe and Tikhomirov and the Dubovitskii–Milyutin theorem. The proof of this principle is based on a simple generalization of the Fermat’s theorem, the smooth-convex extremum principle and the local implicit function theorem. An integro-differential example illustrating the new principle is presented.https://www.mdpi.com/2073-4336/11/4/56extremum principleFermat’s theoremlocal implicit function theorem
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Dariusz Idczak Stanisław Walczak
spellingShingle	Dariusz Idczak Stanisław Walczak An Extremum Principle for Smooth Problems Games extremum principle Fermat’s theorem local implicit function theorem
author_facet	Dariusz Idczak Stanisław Walczak
author_sort	Dariusz Idczak
title	An Extremum Principle for Smooth Problems
title_short	An Extremum Principle for Smooth Problems
title_full	An Extremum Principle for Smooth Problems
title_fullStr	An Extremum Principle for Smooth Problems
title_full_unstemmed	An Extremum Principle for Smooth Problems
title_sort	extremum principle for smooth problems
publisher	MDPI AG
series	Games
issn	2073-4336
publishDate	2020-11-01
description	We derive an extremum principle. It can be treated as an intermediate result between the celebrated smooth-convex extremum principle due to Ioffe and Tikhomirov and the Dubovitskii–Milyutin theorem. The proof of this principle is based on a simple generalization of the Fermat’s theorem, the smooth-convex extremum principle and the local implicit function theorem. An integro-differential example illustrating the new principle is presented.
topic	extremum principle Fermat’s theorem local implicit function theorem
url	https://www.mdpi.com/2073-4336/11/4/56
work_keys_str_mv	AT dariuszidczak anextremumprincipleforsmoothproblems AT stanisławwalczak anextremumprincipleforsmoothproblems AT dariuszidczak extremumprincipleforsmoothproblems AT stanisławwalczak extremumprincipleforsmoothproblems
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An Extremum Principle for Smooth Problems

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