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En mathématiques, un problème d'inéquation variationnelle englobe en les généralisant un certain nombre de problèmes classiques tels que la recherche d'un zéro d'une fonction, la recherche d'un point stationnaire d'un problème d'optimisation, le problème de complémentarité linéaire, etc. Le formalisme a d'abord été introduit pour analyser certaines équations aux dérivées partielles modélisant des problèmes avec contact ou avec frontière libre (problème de Signorini) avant de devenir un cadre formel autonome s'appliquant à des problèmes variés. (fr) In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set. The mathematical theory of variational inequalities was initially developed to deal with equilibrium problems, precisely the Signorini problem: in that model problem, the functional involved was obtained as the first variation of the involved potential energy. Therefore, it has a variational origin, recalled by the name of the general abstract problem. The applicability of the theory has since been expanded to include problems from economics, finance, optimization and game theory. (en) 변동 부등식(variational inequality)은 수학, 게임 이론, 역학, 재료과학 등에서 나타나는 특이한 형태의 부등식을 말한다. 주로 균형점의 개념과 많은 연관 관계가 있다. (ko) Nierówność wariacyjna – pojęcie z pogranicza rachunku wariacyjnego i teorii zbiorów wypukłych. Najogólniejsza postać tego zagadnienia podana poniżej pochodzi od Stuarta Antmana. (pl) |
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http://www.lincei.it/pubblicazioni/catalogo/volume.php%3Flg=e&rid=32885 https://books.google.com/books%3Fid=B1cPRJ3qiw0C&q=An+Introduction+to+Variational+Inequalities+and+Their+Applications https://web.archive.org/web/20150725141516/http:/www.mathunion.org/ICM/ICM1970.3/ http://www3.interscience.wiley.com/journal/113397217/abstract http://gallica.bnf.fr/ark:/12148/bpt6k4012p.image.r=Comptes+Rendus+Academie.f20.langEN http://gallica.bnf.fr/ark:/12148/bpt6k4022z.image.r=Comptes+Rendus+Academie.langEN.f26.pagination https://archive.today/20130105082552/http:/www3.interscience.wiley.com/journal/29240/home%3FCRETRY=1&SRETRY=0 https://archive.today/20130105092629/http:/www3.interscience.wiley.com/journal/113397217/abstract http://www.mathunion.org/ICM/ICM1970.3/ http://www.mathunion.org/ICM/ICM1970.3/Main/icm1970.3.0071.0078.ocr.pdf https://www.scilag.net/problem/G-180630.1 |
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En mathématiques, un problème d'inéquation variationnelle englobe en les généralisant un certain nombre de problèmes classiques tels que la recherche d'un zéro d'une fonction, la recherche d'un point stationnaire d'un problème d'optimisation, le problème de complémentarité linéaire, etc. Le formalisme a d'abord été introduit pour analyser certaines équations aux dérivées partielles modélisant des problèmes avec contact ou avec frontière libre (problème de Signorini) avant de devenir un cadre formel autonome s'appliquant à des problèmes variés. (fr) In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set. The mathematical theory of variational inequalities was initially developed to deal with equilibrium problems, precisely the Signorini problem: in that model problem, the functional involved was obtained as the first variation of the involved potential energy. Therefore, it has a variational origin, recalled by the name of the general abstract problem. The applicability of the theory has since been expanded to include problems from economics, finance, optimization and game theory. (en) 변동 부등식(variational inequality)은 수학, 게임 이론, 역학, 재료과학 등에서 나타나는 특이한 형태의 부등식을 말한다. 주로 균형점의 개념과 많은 연관 관계가 있다. (ko) Nierówność wariacyjna – pojęcie z pogranicza rachunku wariacyjnego i teorii zbiorów wypukłych. Najogólniejsza postać tego zagadnienia podana poniżej pochodzi od Stuarta Antmana. (pl) |
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Inéquation variationnelle (fr) 변동 부등식 (ko) Nierówność wariacyjna (pl) Variational inequality (en) |
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