Reference articles on history, science, culture and more
Surprise meSurprise meSubscribe
Encyclopedia

Gradient method

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated August 13, 2026

In optimization, a gradient method is an algorithm to solve problems of the form

\min _{x\in \mathbb {R} ^{n}}\;f(x)

with the search directions defined by the gradient of the function at the current point. Examples of gradient methods are the gradient descent and the conjugate gradient.

Watch videos about Gradient methodExplainers and documentaries on YouTube (opens in a new tab)

Sources and credits

This article is adapted from the Wikipedia article “Gradient method”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

Fathomly is not affiliated with or endorsed by the Wikimedia Foundation. Spotted a problem? Tell us.

Continue exploring

Related topics

Gradient descent

Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate function.

Stochastic gradient descent

Stochastic gradient descent is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable).

Coordinate descent

Coordinate descent is an optimization algorithm that successively minimizes along coordinate directions to find the minimum of a function. At each iteration, the algorithm determines a coordinate or coordinate block via a coordinate selection rule, then exactly or inexactly minimizes over the corresponding coordinate hyperplane while fixing all other coordinates or coordinate blocks.