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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 Coordinate descent ： ウィキペディア英語版 Coordinate descent Coordinate descent is a non-derivative optimization algorithm. To find a local minimum of a function, one does line search along one coordinate direction at the current point in each iteration. One uses different coordinate directions cyclically throughout the procedure. ==Description== Coordinate descent is based on the idea that the minimization of a multivariable function $F(\backslash mathbf)$ can be achieved by minimizing it along one direction at a time, i.e., solving univariate (or at least much simpler) optimization problems in a loop. In the simplest case of ''cyclic coordinate descent'', one cyclically iterates through the directions, one at a time, minimizing the objective function with respect to each coordinate direction at a time. That is, in each iteration, for each variable of the problem in turn, the algorithm solves the optimization problem :$x^\_i\; =\; \backslash underset\_1,\; \backslash dots,\; x^\_,\; y,\; x^k\_,\; \backslash dots,\; x^k\_n).$ Thus, one begins with an initial guess $\backslash mathbf^0$ for a local minimum of $F$, and get a sequence $\backslash mathbf^0,\; \backslash mathbf^1,\; \backslash mathbf^2,\; \backslash dots$ iteratively. By doing line search in each iteration, one automatically has :$F(\backslash mathbf^0)\backslash ge\; F(\backslash mathbf^1)\backslash ge\; F(\backslash mathbf^2)\backslash ge\; \backslash dots.$ It can be shown that this sequence has similar convergence properties as steepest descent. No improvement after one cycle of line search along coordinate directions implies a stationary point is reached. This process is illustrated below. File:coordinate descent.jpg 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「Coordinate descent」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.