Problem 1278 (difficulty: 9/10)

Given \(\displaystyle F:\R^p\to\R\) twice differentiable convex function we are looking for the minimum of \(\displaystyle F\) using the conjugate gradient method: start with \(\displaystyle x_0\) and let

\(\displaystyle x_{n+1} = x_n - c(x_n)\cdot \mathrm{grad}f(x_n), \)

where \(\displaystyle c(x_n)\) is computed from the first and second derivatives of \(\displaystyle f\) at \(\displaystyle x_n\).

(a) What is a good choice for \(\displaystyle c(x_n)\)?

(b) Prove that method works for quadratic forms.

Give me another random problem!