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Optimization : Standard Conjugate Gradient Algorithm

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.