翻訳と辞書 Words near each other ・ Backyard Broadcasting ・ Backyard cricket ・ Backyard Dog ・ Backyard Dogs ・ Backyard Farmer ・ Backyard Farms ・ Backyard Football ・ Backtrack ・ Backtrack (2015 film) ・ BackTrack (magazine) ・ Backtrack (novel) ・ Backtrack (song) ・ Backtrack Music ・ Backtrackin' ・ Backtracking ・ Backtracking line search ・ Backtracks (AC/DC album) ・ Backtracks (Poco album) ・ Backtrax USA ・ BackTweets ・ BackType ・ Backup ・ Backup (disambiguation) ・ Backup (software) ・ Backup (TV series) ・ Backup and Restore ・ Backup band ・ Backup battery ・ Backup camera ・ Backup dancer 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 Backtracking line search ： ウィキペディア英語版 Backtracking line search In (unconstrained) minimization, a backtracking line search, a search scheme based on the Armijo–Goldstein condition, is a line search method to determine the maximum amount to move along a given search direction. It involves starting with a relatively large estimate of the step size for movement along the search direction, and iteratively shrinking the step size (i.e., "backtracking") until a decrease of the objective function is observed that adequately corresponds to the decrease that is expected, based on the local gradient of the objective function. ==Motivation== Given a starting position $\backslash mathbf$ and a search direction $\backslash mathbf$, the task of a line search is to determine a step size $\backslash alpha$ that adequately reduces the objective function $f:\backslash mathbb\; R^n\backslash to\backslash mathbb\; R$ (assumed smooth), i.e., to find a value of $\backslash alpha$ that reduces $f(\backslash mathbf+\backslash alpha\backslash ,\backslash mathbf)$ relative to $f(\backslash mathbf)$. However, it is usually undesirable to devote substantial resources to finding a value of $\backslash alpha$ to precisely minimize $f$. This is because the computing resources needed to find a more precise minimum along one particular direction could instead be employed to identify a better search direction. Once an improved starting point has been identified by the line search, another subsequent line search will ordinarily be performed in a new direction. The goal, then, is just to identify a value of $\backslash alpha$ that provides a reasonable amount of improvement in the objective function, rather than to find the actual minimizing value of $\backslash alpha$. The backtracking line search starts with a large estimate of $\backslash alpha$ and iteratively shrinks it. The shrinking continues until a value is found that is small enough to provide a decrease in the objective function that adequately matches the decrease that is expected to be achieved, based on the local function gradient $\backslash nabla\; f(\backslash mathbf)\backslash ,.$ Define the local slope of the function of $\backslash alpha$ along the search direction $\backslash mathbf$ as $m\; =\; \backslash mathbf^\backslash ,\backslash nabla\; f(\backslash mathbf)\backslash ,.$ It is assumed that $\backslash mathbf$ is a direction in which some local decrease is possible, i.e., it is assumed that . Based on a selected control parameter $c\backslash ,\backslash in\backslash ,(0,1)$, the Armijo–Goldstein condition tests whether a step-wise movement from a current position $\backslash mathbf$ to a modified position $\backslash mathbf+\backslash alpha\backslash ,\backslash mathbf$ achieves an adequately corresponding decrease in the objective function. The condition is fulfilled if $f(\backslash mathbf+\backslash alpha\backslash ,\backslash mathbf)\backslash leq\; f(\backslash mathbf)+\backslash alpha\backslash ,c\backslash ,m\backslash ,.$ This condition, when used appropriately as part of a line search, can ensure that the step size is not excessively large. However, this condition is not sufficient on its own to ensure that the step size is nearly optimal, since any value of $\backslash displaystyle\; \backslash alpha$ that is sufficiently small will satisfy the condition. Thus, the backtracking line search strategy starts with a relatively large step size, and repeatedly shrinks it by a factor $\backslash tau\backslash ,\backslash in\backslash ,(0,1)$ until the Armijo–Goldstein condition is fulfilled. The search will terminate after a finite number of steps for any positive values of $c$ and $\backslash tau$ that are less than 1. For example, Armijo used for both $c$ and $\backslash tau$ in a paper he published in 1966. 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「Backtracking line search」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.