Minimize Rosenbrock Function With Conjugate Gradient Method

Asked Aug 13 '13 at 08:35

Active Aug 13 '13 at 08:35

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I want to minimize

$$ f(x,y) = (1-x)^2 + 100(y-x^2)^2 $$

For the conjugate gradient method I need the quadratic form

$$ f(\mathbf{x}) = \frac{1}{2}\mathbf{x}^{\text{T}}\mathbf{A}\mathbf{x} - \mathbf{x}^{\text{T}}\mathbf{b} $$

Is this even possible to bring the Rosenbrock function in this form? If yes, how would I have to do this?

asked Aug 13 '13 at 08:35

Philipp

2

No, it is not possible. You need the nonlinear conjugate gradient method; see Wikipedia or Ch. 14 of Jonathan Shewchuk's introduction to CG. – Aug 13 '13 at 08:45
Thank you, if you want to put this in an answer I can give you precious internet points :) – Philipp Aug 13 '13 at 09:07

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