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Gradient-related : ウィキペディア英語版
Gradient-related

Gradient-related is a term used in multivariable calculus to describe a direction. A direction sequence \ is ''gradient-related'' to \ if for any subsequence \_ that converges to a nonstationary point, the corresponding subsequence \_ is bounded and satisfies''
\limsup_ \nabla f(x^k)'d^k <0.
A gradient-related direction is usually encountered in the gradient-based iterative optimisation of a function f. At each iteration k the current vector is x^k and we move in the direction d^k, thus generating a sequence of directions.
It is easy to guarantee that the directions we generate are gradient-related, by for example setting them equal to the gradient at each point.



抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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