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

[Lingyun Qiu]

I think *KSPSetPostSolve * is to add a post-processing after all the
iterations inside KSPSolve finish. I need to modify the iterates inside
KSPSolve or the linear solver.
I just realize that this nonlinear operation will also affect the Krylov
subspaces. Perhaps I should look for some other linear solver instead of
KSPSolve. Comments are welcome.

On Thu, Apr 7, 2016 at 2:24 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Thu, Apr 7, 2016 at 2:13 PM, Lingyun Qiu <qiu.lingyun at gmail.com> wrote:
>
>> 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.
>>
>
> Are you asking for something like this:
>
>
> http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetPostSolve.html
>
>   Thanks,
>
>      Matt
>
>
>> 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
>>
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
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