# Broyden family

This is a family of algorithms to solve an unconstrained nonlinear program where the objective function is in $LaTeX: C^2$;. The algorithms in this family differ by how they update the approximation of the hessian inverse (assumed to exist). These are of the form:
$LaTeX: H = aH^{\mbox{BFGS}} + (1-a)H^{\mbox{DFP}},$
with the two matrices being the Broyden-Fletcher-Goldfarb-Shanno update (BFGS) and the Davidon-Fletcher-Powell update (DFP), respectively. If $LaTeX: a$ is in $LaTeX: [0, 1]$, this is called the Broyden convex family.