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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 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 : Thus, one begins with an initial guess for a local minimum of , and get a sequence iteratively. By doing line search in each iteration, one automatically has : 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
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