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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Slater's condition ： ウィキペディア英語版 Slater's condition In mathematics, Slater's condition (or Slater condition) is a sufficient condition for strong duality to hold for a convex optimization problem, named after Morton L. Slater. Informally, Slater's condition states that the feasible region must have an interior point (see technical details below). Slater's condition is a specific example of a constraint qualification. In particular, if Slater's condition holds for the primal problem, then the duality gap is 0, and if the dual value is finite then it is attained. ==Details== Given the problem :$\backslash text\backslash ;\; f\_0(x)$ :$\backslash text\backslash$ ::$f\_i(x)\; \backslash le\; 0\; ,\; i\; =\; 1,\backslash ldots,m$ ::$Ax\; =\; b$ with $f\_0,\backslash ldots,f\_m$ convex (and therefore a convex optimization problem). Then Slater's condition implies that strong duality holds if there exists an $x\; \backslash in\; \backslash operatorname(D)$ (where relint is the relative interior and $D\; =\; \backslash cap\_^m\; \backslash operatorname(f\_i)$) such that : and :$Ax\; =\; b.\backslash ,$ If the first $k$ constraints, $f\_1,\backslash ldots,f\_k$ are linear functions, then strong duality holds if there exists an $x\; \backslash in\; \backslash operatorname(D)$ such that :$f\_i(x)\; \backslash le\; 0,\; i\; =\; 1,\backslash ldots,k,$ : and :$Ax\; =\; b.\backslash ,$〔 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「Slater's condition」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.