# 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 .

https://brainmass.com/math/optimization/optimization-standard-conjugate-gradient-algorithm-11031

#### 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 ...

#### Solution Summary

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