# DFP method

This is a method to solve an unconstrained nonlinear program that proceeds as follows.

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