[petsc-users] [tao] General L1,L2 optimization

[Dener, Alp]

Hi Hansol,

We don’t have a Levenberg-Marquardt method available, and if the PETSc/TAO manual says otherwise, that may be misleading. Let me know where you saw that and I can take a look and fix it.

In the meantime, if you want to solve a least-squares problem, the master branch of PETSc on Bitbucket has a bound-constrained regularized Gauss-Newton (TAOBRGN) method available. The only available regularization right now is an L2 proximal point Tikhonov regularizer. There are ongoing efforts to support an L1 regularizer, and also the ability for users to define their own, but these have not made it into the master branch yet. We’re working on it and should be in for the next major PETSc release in the Spring.

If you’d like to use that method, you need to set the Tao type to TAOBRGN and then go through the TaoSetResidualRoutine() and TaoSetJacobianResidualRoutine() interfaces to define your problem.

In general, you can use other TAO algorithms (e.g.: BNLS, BQNLS, etc.) with your own regularization term by embedding it into the objective, gradient and Hessian (if applicable) evaluation callbacks. The caveat is that your regularizer needs to be C1 continuous for first-order methods and C2 continuous for second order methods. This typically limits you to L2-norm regularizers. There is no support yet for L1-norm regularizers, but as I said, we’re working on it right now and it should be available in a couple of months.

Hope that helps,
——
Alp Dener
Argonne National Laboratory
https://www.anl.gov/profile/alp-dener



On Jan 24, 2019, at 2:57 PM, David via petsc-users <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>> wrote:

Hi. I was wondering whether there was some kind of general consensus about

the currently-best-implemented L1, L2 norm regularization for petsc/tao
that has been implemented.

Naively, I would shoot for Levenberg-Marquardt for some kind of random
matrix, or even generic

finite-difference stencil problem. (but it seems like LM is yet to be
implemented, but only on petsc manual pdf?)

Or perhaps, of the implemented ones, LMVM seems to work well, at least
on my local machine.

In any due case, I would highly appreciate the input and opinion about
these matters.


Thanks.



Hansol Suh,

PhD Student


Georgia Institute of Technology


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