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January 20th, 2009, 01:46 AM   #1
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Differentiating the gradient?

Hi!

This problem arises when trying to do a Newton-step in an optimization problem:

Stating from t0=0 i wish to take the step t1 = -dP'(0)/dt / dP''(0)/dt , where P=f(x+td) and f is a given function.

Thus, dP(x)/dt must equal grad(f(x+td))'*d, which for t=0 -> P'(0)=grad(f(x))'*d. Everytinh fine so far.

But how to derive dP''(0)/dt?? It's essentially a question about differentiating the gradient, something I am not sure as to how to go about.

Thanks in advance
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January 20th, 2009, 02:20 AM   #2
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Re: Differentiating the gradient?

On a second thought, though, couldn't this be written as the derivative component-wise? I.e. with my P(t) as:
dP''(0)/dt=laplacian(f(x+td))'*d
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