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Generating of conjugate directions For a quadratic function

Generating of conjugate directions For a quadratic function

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Generating of conjugate directions For a quadratic function

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  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. Algorithm of the Modified Powell’s 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->k+1, repeat step 2 to step 4, until the convergence with a specified accuracy is reached.

  3. Modified Powell’s Mehtod(the 1st cycle)

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