Originally Posted by
fp04 Sorry, maybe I wasn't clear. Let me give you the entire problem I'm solving....
I work in the field of MRI Physics. I need to perform the following optimisation:
min{m1,m2} l2norm(Fm1 - y1) + l2norm(Fm2 - y2) + lambda* l1norm(f(m1,m2))
F is the Fourier matrix, m1 and m2 are vectors of length of 512^2, y1 and y2 are vectors of the same length and lambda is a normalisation constant.
The function f divides vectors m1 and m2 in an elementwise manner.
As the vectors are so large I would like to use a conjugate gradient method to perform the optimisation. Therefore, I need to take the derivative of the function w.r.t m1 and m2. However, the elementwise division of m1 and m2 is undifferentiable.
So, I need to rewrite the elementwise division of two vectors in a way which is differentiable. Therein lies the problem!
Is this clear...?