These integrals can be approximated by the method of steepest descent.

Some asymptotic representations can then be derived by a standard application of the method of steepest descent.

The simplest procedures use the gradient descent technique, sometimes also known as the method of steepest descent.

The formula may also be obtained by repeated integration by parts, and the leading term can be found through the method of steepest descent.

When the objective function is differentiable, subgradient methods for unconstrained problems use the same search direction as the method of steepest descent.

When known as the latter, gradient descent should not be confused with the method of steepest descent for approximating integrals.

Gradient descent is also known as steepest descent, or the method of steepest descent.

Method of steepest descent employs a partition of unity to construct asymptotics of integrals.

Rigorous treatments of the method of steepest descent and the method of stationary phase, amongst others, are based on the Riemann-Lebesgue lemma.

The method of steepest descent was first published by , who used it to estimate Bessel functions and pointed out that it occurred in the unpublished note about hypergeometric functions.

Asymptotic expansions typically arise in the approximation of certain integrals (Laplace's method, saddle-point method, method of steepest descent) or in the approximation of probability distributions (Edgeworth series).

There exists a method for extracting the asymptotic behavior of solutions of Riemann-Hilbert problems, analogous to the method of stationary phase and the method of steepest descent applicable to exponential integrals.

One version of the method of steepest descent deforms the contour of integration so that it passes through a zero of the derivative g'(z) in such a way that on the contour g is (approximately) real and has a maximum at the zero.