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Clarify task of descent classes #69

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Jul 18, 2024
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Clarify task of descent classes #69

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2 changes: 1 addition & 1 deletion docs/api/searches/introduction.md
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Expand Up @@ -10,7 +10,7 @@ Consider a function $f \colon \mathbb{R}^n \to \mathbb{R}$, that we would like t

**Descents**

Descents consume information about values+gradients+Hessians etc. of $f$, along with this scalar value, and give the size of the update to make. This corresponds to `-scalar * gradient` for gradient descent, `-scalar * (Hessian^{-1} gradient)` for (Gauss--)Newton algorithms, the distance along the dogleg path with Dogleg, `(Jacobian^T Jacobian + scalar * I)^{-1} gradient` for Levenberg--Marquardt (damped Newton), and so on. [Although `Jacobian^T Jacobian` isn't actually materialised -- the implementation does the smart thing and solves a least-squares problem using QR.]
Descents consume information about values+gradients+Hessians etc. of $f$, along with this scalar value, and compute the update to make. This corresponds to `-scalar * gradient` for gradient descent, `-scalar * (Hessian^{-1} gradient)` for (Gauss--)Newton algorithms, the distance along the dogleg path with Dogleg, `(Jacobian^T Jacobian + scalar * I)^{-1} gradient` for Levenberg--Marquardt (damped Newton), and so on. [Although `Jacobian^T Jacobian` isn't actually materialised -- the implementation does the smart thing and solves a least-squares problem using QR.]

**Examples**

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