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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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