Broyden's method for optimization of a function of multiple variables

Definition

Suppose $x_{1},x_{2},\dots ,x_{m}$ are variables and $f$ is a real-valued function of these variables. Broyden's method for optimization for $f$ uses Broyden's method for root-finding for a vector-valued function of a vector variable, applied to the gradient vector $\nabla f$.

The translation from root-finding to optimization is similar to the way Newton's method for optimization of a function of multiple variables relies on Newton's method for root-finding for a vector-valued function of a vector variable.