Wikipedia
Gradient-related
Gradient-related is a term used in multivariable calculus to describe a direction. A direction sequence {d} is gradient-related to {x} if for any subsequence {x} that converges to a nonstationary point, the corresponding subsequence {d} is bounded and satisfies''
limsup∇f(x)ʹd < 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 and we move in the direction d, 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.
Category:Vector calculus