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

[Jed Brown]

Lingyun Qiu <qiu.lingyun at gmail.com> writes:

> 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.e., a single KSPSolve because the optimization problem is quadratic?

> 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.

But outside the KSPSolve, not at each iteration of the KSPSolve...

B is a nonlinear operation, so you can't put it inside KSP.  You could
put it inside SNES (perhaps with nonlinear preconditioning, NGMRES or
QN), but I don't think that's what you're asking for here.
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