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In optimization, a descent direction is a vector that, in the sense below, moves us closer towards a local minimum of our objective function . Suppose we are computing by an iterative method, such as line search. We define a descent direction at the th iterate to be any such that , where denotes the inner product. The motivation for such an approach is that small steps along guarantee that is reduced, by Taylor's theorem. Using this definition, the negative of a non-zero gradient is always a descent direction, as . Numerous methods exist to compute descent directions, all with differing merits. For example, one could use gradient descent or the conjugate gradient method. More generally, if is a positive definite matrix, then is a descent direction at . This generality is used in preconditioned gradient descent methods. 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「descent direction」の詳細全文を読む スポンサード リンク
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