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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 Wolfe conditions ： ウィキペディア英語版 Wolfe conditions In the unconstrained minimization problem, the Wolfe conditions are a set of inequalities for performing inexact line search, especially in quasi-Newton methods, first published by Philip Wolfe in 1969. In these methods the idea is to find ::$\backslash min\_x\; f(\backslash mathbf)$ for some smooth $f:\backslash mathbb\; R^n\backslash to\backslash mathbb\; R$. Each step often involves approximately solving the subproblem ::$\backslash min\_\; f(\backslash mathbf\_k\; +\; \backslash alpha\; \backslash mathbf\_k)$ where $\backslash mathbf\_k$ is the current best guess, $\backslash mathbf\_k\; \backslash in\; \backslash mathbb\; R^n$ is a search direction, and $\backslash alpha\; \backslash in\; \backslash mathbb\; R$ is the step length. The inexact line searches provide an efficient way of computing an acceptable step length $\backslash alpha$ that reduces the objective function 'sufficiently', rather than minimizing the objective function over $\backslash alpha\backslash in\backslash mathbb\; R^+$ exactly. A line search algorithm can use Wolfe conditions as a requirement for any guessed $\backslash alpha$, before finding a new search direction $\backslash mathbf\_k$. ==Armijo rule and curvature== Denote a univariate function $\backslash phi$ restricted to the direction $\backslash mathbf\_k$ as $\backslash phi(\backslash alpha)=f(\backslash mathbf\_k+\backslash alpha\backslash mathbf\_k)$. A step length $\backslash alpha\_k$ is said to satisfy the ''Wolfe conditions'' if the following two inequalities hold: :i) $f(\backslash mathbf\_k+\backslash alpha\_k\backslash mathbf\_k)\backslash leq\; f(\backslash mathbf\_k)+c\_1\backslash alpha\_k\backslash mathbf\_k^\backslash nabla\; f(\backslash mathbf\_k)$, :ii) $\backslash mathbf\_k^\backslash nabla\; f(\backslash mathbf\_k+\backslash alpha\_k\backslash mathbf\_k)\; \backslash geq\; c\_2\backslash mathbf\_k^\backslash nabla\; f(\backslash mathbf\_k)$, with $c\_1$ is usually chosen to be quite small while $c\_2$ is much larger; Nocedal gives example values of $c\_1=10^$ and $c\_2=0.9$ for Newton or quasi-Newton methods and $c\_2=0.1$ for the nonlinear conjugate gradient method. Inequality i) is known as the Armijo rule and ii) as the curvature condition; i) ensures that the step length $\backslash alpha\_k$ decreases $f$ 'sufficiently', and ii) ensures that the slope has been reduced sufficiently. 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「Wolfe 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.