翻訳と辞書 Words near each other ・ Fritz Nallinger ・ Fritz Neugebauer ・ Fritz Neuland ・ Fritz Isser ・ Fritz J. Raddatz ・ Fritz Jack ・ Fritz Jacobeit ・ Fritz Jacobsen ・ Fritz Jakobsson ・ Fritz Janschka ・ Fritz Jean ・ Fritz Jenssen ・ Fritz Joachim Weyl ・ Fritz Johansson ・ Fritz John ・ Fritz John conditions ・ Fritz Joost ・ Fritz Joubert Duquesne ・ Fritz Julius Kuhn ・ Fritz Jüptner-Jonstorff ・ Fritz Kachler ・ Fritz Kahn ・ Fritz Kaiser ・ Fritz Kalkbrenner ・ Fritz Kampers ・ Fritz Karl ・ Fritz Kasparek ・ Fritz Kater ・ Fritz Katz ・ Fritz Katzmann Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fritz John conditions ： ウィキペディア英語版 Fritz John conditions The Fritz John conditions (abbr. FJ conditions), in mathematics, are a necessary condition for a solution in nonlinear programming to be optimal. They are used as lemma in the proof of the Karush–Kuhn–Tucker conditions, but they are relevant on their own. We consider the following optimization problem: :$$ \begin \text & f(x) \, \\ \text & g_i(x) \ge 0,\ i \in \left \\\ & h_j(x) = 0, \ j \in \left \ \end where ''ƒ'' is the function to be minimized, $g\_i$ the inequality constraints and $h\_j$ the equality constraints, and where, respectively, $\backslash mathcal$, $\backslash mathcal$ and $\backslash mathcal$ are the indices set of inactive, active and equality constraints and $x^$ * is an optimal solution of $f$, then there exists a non-zero vector $\backslash lambda=(\backslash lambda\; \_1,\; \backslash lambda\; \_2,\backslash dots,\backslash lambda\; \_n)$ such that: :$\backslash begin$ \lambda_0 \nabla f(x^ *) = \sum\limits_ \lambda_i \nabla g_i(x^ *) + \sum\limits_'\cup\ \\() \exists i\in \left( \ \backslash \mathcal \right) \left( \lambda_i \ne 0 \right) \end $\backslash lambda\_0>0$ if the $\backslash nabla\; g\_i\; (i\backslash in\backslash mathcal\text{'})$ and $\backslash nabla\; h\_i\; (i\backslash in\backslash mathcal)$ are linearly independent or, more generally, when a constraint qualification holds. Named after Fritz John, these conditions are equivalent to the Karush–Kuhn–Tucker conditions in the case $\backslash lambda\_0\; >\; 0$. ==References== * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fritz John conditions」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.