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# Optimization : Standard Conjugate Gradient Algorithm

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Please see the attached file for the fully formatted problems.

We consider the function J defined as

and .

1) Prove mathematically that K is strictly convex.
2) Descibe the two algorithms of conjugated gradient for this function K.
3) Are they descending algorithms?
4) Choose one of them, and choose a method to obtain the step in each iteration.
Write the first three iterations in detail for .

##### Solution Summary

The standard conjugate gradient algorithm is employed to solve optimization problems.

##### Solution Preview

Follow the standard conjugate gradient algorithm. Please see the attached file.

We consider the function J defined as

and .

1) Prove mathematically that K is trictly convex.
2) Descibe the two algorithms of conjugated gradiant for this function K.
3) Are they descending algorithms?
4) Choose one of them, and choose a method to obtain the step in each iteration.
Write the first three iterations in detail for .

1) The function ...

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