January 20th, 2009, 01:46 AM  #1 
Newbie Joined: Jan 2009 Posts: 2 Thanks: 0  Differentiating the gradient?
Hi! This problem arises when trying to do a Newtonstep in an optimization problem: Stating from t0=0 i wish to take the step t1 = dP'(0)/dt / d²P''(0)/dt² , 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 d²P''(0)/dt²?? It's essentially a question about differentiating the gradient, something I am not sure as to how to go about. Thanks in advance 
January 20th, 2009, 02:20 AM  #2 
Newbie Joined: Jan 2009 Posts: 2 Thanks: 0  Re: Differentiating the gradient?
On a second thought, though, couldn't this be written as the derivative componentwise? I.e. with my P(t) as: d²P''(0)/dt²=laplacian(f(x+td))'*d² 

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