DAVIDON-FLETCHER-POWELL

Davidon-Fletcher-Powell (DFP) method - This is a method to solve an unconstrained nonlinear program that proceeds as follows.

Start with any symmetric, negative definite matrix , say H (e.g., -I), and any point, say x. Compute g=grad_f(x), and set each of the following:
1. direction: d = -Hg.
2. step size: s in argmax(f(x + td): t >= 0).
3. change in position: p = sd.
4. new point and gradient: x' = x + p and g' = grad_f(x').
5. change in gradient: q = g' - g.
6. Replace x with x' and update H by the DFP update to complete the iteration.