DFP method

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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.

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