Broyden family

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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:

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.

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