gradient and hessian of norm-1?

Question

For solving an optimization problem in MATLAB I need to calculate the gradient and hessian of the following norm-1 function:

norm1(A.x)

here x is the parameter (n-by-1 vector) and A is a known fixed matrix (n-by-n matrix). Anybody have seen similar calculation to point me at?

Thanks much.

Answer 1

The norm 1 is a sum of absolute values. And the partial derivative of an absolute value is x/|x| so you if you have A you will have something like A_ij x_i/|x_i|