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What (who) is steepest-descent procedure - definition
![An animation showing the first 83 iterations of gradient descent applied to this example. Surfaces are [[isosurface]]s of <math>F(\mathbf{x}^{(n)})</math> at current guess <math>\mathbf{x}^{(n)}</math>, and arrows show the direction of descent. Due to a small and constant step size, the convergence is slow.](https://commons.wikimedia.org/wiki/Special:FilePath/Gradient Descent Example Nonlinear Equations.gif?width=200 "An animation showing the first 83 iterations of gradient descent applied to this example. Surfaces are [[isosurface]]s of <math>F(\mathbf{x}^{(n)})</math> at current guess <math>\mathbf{x}^{(n)}</math>, and arrows show the direction of descent. Due to a small and constant step size, the convergence is slow.")
![Illustration of gradient descent on a series of [[level set]]s](https://commons.wikimedia.org/wiki/Special:FilePath/Gradient descent.svg?width=200 "Illustration of gradient descent on a series of [[level set]]s")
.jpg?width=200 "Fog in the mountains")
![The steepest descent algorithm applied to the [[Wiener filter]]<ref>Haykin, Simon S. Adaptive filter theory. Pearson Education India, 2008. - p. 108-142, 217-242</ref>](https://commons.wikimedia.org/wiki/Special:FilePath/Steepest descent.png?width=200 "The steepest descent algorithm applied to the [[Wiener filter]]<ref>Haykin, Simon S. Adaptive filter theory. Pearson Education India, 2008. - p. 108-142, 217-242</ref>")
Wikipedia
In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a local maximum of that function; the procedure is then known as gradient ascent. It is particularly useful in machine learning for minimizing the cost or loss function. Despite its simplicity and efficiency, gradient descent has some limitations and variations have been developed to overcome these limitations. Overall, gradient descent has revolutionized various fields and continues to be an active area of research and development.
Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Haskell Curry in 1944, with the method becoming increasingly well-studied and used in the following decades.
