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Finally, I introduce the specialized notation I like
for optimization manipulations.
First, I omit bold on vectors.
Second, when a vector is transformed by the operator ,I denote the transformed vector by an upper-case letter.
Thus and .Let the scalar denote the distance moved along the gradient.
In this notation, perturbations of are
| |
(6) |

A steepest descent method amounts to:
- 1.
- Find the gradient using (5)
- 2.
- Compute and
- 3.
- Maximize the ratio of scalars in (6)
by any crude method such as interval division.
- 4.
- Repeat.

A conjugate-gradient-like method is like the steepest descent method
supplementing the gradient by another vector,
the vector of the previous step.
Michael Saunders suggested the Pollack-Ribier (sp) method
and gave me a Fortran subroutine for the line search.

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Stanford Exploration Project

12/18/1997