[petsc-users] L1 or projection type regularization with PETSc

[Lingyun Qiu]

Dear all,

I am working an optimization problem as
min_x  ||Ax - b||_2^2 + alpha ||x||_1

For the fidelity term, we use L2 norm.  We use L1 norm for the
regularization term. Without regularization term, i.e., alpha=0, we
iteratively solve the problem as
x_k+1 = KSP(x_k).

I plan to use the split Bregman method to solve the regularized problem. It
reads as,
y_k+1 = KSP(x_k)
x_k+1 = B(y_k+1)
Here B() is the function related to the Bregman method. It works as a
post-processing of the iterates.

I am wondering is there a way to combine this post-processing with the KSP
solver? A brute-force way is modify the initial guess and set the max
iteration number to 1.
This is also related to the projection type regularization:
min_{x in subspace G} ||Ax-b||^2_2
The scheme is
y_k+1 = KSP(x_k)
x_k+1 = P_G(y_k+1)
where P_G is the projection to subspace G.

Lingyun Qiu
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20160407/1fb77adb/attachment.html>