[petsc-users] Integrating TAO into SNES and TS

Tue Sep 1 03:11:04 CDT 2015

Barry,

That's good to know thanks.

On a related note, is it possible for VI to one day include linear equality
constraints?

Thanks,
Justin

On Mon, Aug 31, 2015 at 7:13 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
> > On Aug 31, 2015, at 7:36 PM, Justin Chang <jychang48 at gmail.com> wrote:
> >
> > Coming back to this,
> >
> > Say I now want to ensure the DMP for advection-diffusion equations. The
> linear operator is now asymmetric and non-self-adjoint (assuming I do
> something like SUPG or finite volume), meaning I cannot simply solve this
> problem without any manipulation (e.g. normalizing the equations) using
> TAO's optimization solvers. Does this statement also hold true for SNESVI?
>
>   SNESVI doesn't care about symmetry etc
>
> >
> > Thanks,
> > Justin
> >
> > On Fri, Apr 3, 2015 at 7:38 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> >
> > > On Apr 3, 2015, at 7:35 PM, Justin Chang <jchang27 at uh.edu> wrote:
> > >
> > > I guess I will have to write my own code then :)
> > >
> > > I am not all that familiar with Variational Inequalities at the
> moment, but if my Jacobian is symmetric and positive definite and I only
> have lower and upper bounds, doesn't the problem simply reduce to that of a
> convex optimization? That is, with SNES act as if it were Tao?
> >
> >   Yes, I think that is essentially correctly.
> >
> >   Barry
> >
> > >
> > > On Fri, Apr 3, 2015 at 6:35 PM, Barry Smith <bsmith at mcs.anl.gov>
> wrote:
> > >
> > >   Justin,
> > >
> > >    We haven't done anything with TS to handle variational
> inequalities. So you can either write your own backward Euler (outside of
> TS) that solves each time-step problem either as 1) an optimization problem
> using Tao or 2) as a variational inequality using SNES.
> > >
> > >    More adventurously you could look at the TSTHETA code in TS (which
> is a general form that includes Euler, Backward Euler and Crank-Nicolson
> and see if you can add the constraints to the SNES problem that is solved;
> in theory this is straightforward but it would require understanding the
> current code (which Jed, of course, overwrote :-). I think you should do
> this.
> > >
> > >   Barry
> > >
> > >
> > > > On Apr 3, 2015, at 12:31 PM, Justin Chang <jchang27 at uh.edu> wrote:
> > > >
> > > > I am solving the following anisotropic transient diffusion equation
> subject to 0 bounds:
> > > >
> > > > du/dt = div[D*grad[u]] + f
> > > >
> > > > Where the dispersion tensor D(x) is symmetric and positive definite.
> This formulation violates the discrete maximum principles so one of the
> ways to ensure nonnegative concentrations is to employ convex optimization.
> I am following the procedures in Nakshatrala and Valocchi (2009) JCP and
> Nagarajan and Nakshatrala (2011) IJNMF.
> > > >
> > > > The Variational Inequality method works gives what I want for my
> transient case, but what if I want to implement the Tao methodology in TS?
> That is, what TS functions do I need to set up steps a) through e) for each
> time step (also the Jacobian remains the same for all time steps so I would
> only call this once). Normally I would just call TSSolve() and let the
> libraries and functions do everything, but I would like to incorporate
> TaoSolve into every time step.
> > > >
> > > > Thanks,
> > > >
> > > > --
> > > > Justin Chang
> > > > PhD Candidate, Civil Engineering - Computational Sciences
> > > > University of Houston, Department of Civil and Environmental
> Engineering
> > > > Houston, TX 77004
> > > > (512) 963-3262
> > > >
> > > > On Thu, Apr 2, 2015 at 6:53 PM, Barry Smith <bsmith at mcs.anl.gov>
> wrote:
> > > >
> > > >   An alternative approach is for you to solve it as a (non)linear
> variational inequality. See src/snes/examples/tutorials/ex9.c
> > > >
> > > >   How you should proceed depends on your long term goal. What
> problem do you really want to solve? Is it really a linear time dependent
> problem with 0 bounds on U? Can the problem always be represented as an
> optimization problem easily? What are  and what will be the properties of
> K? For example if K is positive definite then likely the bounds will remain
> try without explicitly providing the constraints.
> > > >
> > > >   Barry
> > > >
> > > > > On Apr 2, 2015, at 6:39 PM, Justin Chang <jchang27 at uh.edu> wrote:
> > > > >
> > > > > Hi everyone,
> > > > >
> > > > > I have a two part question regarding the integration of the
> following optimization problem
> > > > >
> > > > > min 1/2 u^T*K*u + u^T*f
> > > > > S.T. u >= 0
> > > > >
> > > > > into SNES and TS
> > > > >
> > > > > 1) For SNES, assuming I am working with a linear FE equation, I
> have the following algorithm/steps for solving my problem
> > > > >
> > > > > a) Set an initial guess x
> > > > > b) Obtain residual r and jacobian A through functions
> SNESComputeFunction() and SNESComputeJacobian() respectively
> > > > > c) Form vector b = r - A*x
> > > > > d) Set Hessian equal to A, gradient to A*x, objective function
> value to 1/2*x^T*A*x + x^T*b, and variable (lower) bounds to a zero vector
> > > > > e) Call TaoSolve
> > > > >
> > > > > This works well at the moment, but my question is there a more
> "efficient" way of doing this? Because with my current setup, I am making a
> rather bold assumption that my problem would converge in one SNES iteration
> without the bounded constraints and does not have any unexpected
> nonlinearities.
> > > > >
> > > > > 2) How would I go about doing the above for time-stepping
> problems? At each time step, I want to solve a convex optimization subject
> to the lower bounds constraint. I plan on using backward euler and my
> resulting jacobian should still be compatible with the above optimization
> problem.
> > > > >
> > > > > Thanks,
> > > > >
> > > > > --
> > > > > Justin Chang
> > > > > PhD Candidate, Civil Engineering - Computational Sciences
> > > > > University of Houston, Department of Civil and Environmental
> Engineering
> > > > > Houston, TX 77004
> > > > > (512) 963-3262
> > > >
> > > >
> > > >
> > > >
> > > > --
> > > > Justin Chang
> > > > PhD Candidate, Civil Engineering - Computational Sciences
> > > > University of Houston, Department of Civil and Environmental
> Engineering
> > > > Houston, TX 77004
> > > > (512) 963-3262
> > >
> > >
> > >
> > >
> > > --
> > > Justin Chang
> > > PhD Candidate, Civil Engineering - Computational Sciences
> > > University of Houston, Department of Civil and Environmental
> Engineering
> > > Houston, TX 77004
> > > (512) 963-3262
> >
> >
>
>
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