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Generating of conjugate directions

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Generating of conjugate directions For a quadratic function and two arbitrary points , and a specified direction ,let denotes the minimum ... – PowerPoint PPT presentation

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Date added: 30 December 2018
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Title: Generating of conjugate directions

1
• Generating of conjugate directions
• For a quadratic function
• and two arbitrary points , and
a specified direction ,let denotes
the minimum point of on the line starting
at along and the minimum point
on the line starting at along , then
the directions and ( - ) are
Q-conjugate.

2

3
• Algorithm of the Modified Powells Method
• 1. Given a starting point ,for each
coordinate direction, generate the points at
which the minimum of the objective function
occurs, denotes them by
• , , .
• 2. Find the index corresponding to the
direction of the above univariate search which
yields the largest decrease from to
.
• 3. Calculate the pattern direction
and determine the point at
which the minimization of f along the pattern
direction occurs.
• 4. Check the following criterion to see if the
search direction set needs to be undated.
• 5. k-gtk1, repeat step 2 to step 4, until the
convergence with a specified accuracy is reached.

4
Modified Powells Mehtod(the 1st cycle)
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