[petsc-users] Integrating TAO into SNES and TS

[Matthew Knepley]

On Tue, Sep 1, 2015 at 3:11 AM, Justin Chang <jychang48 at gmail.com> wrote:

> Barry,
>
> That's good to know thanks.
>
> On a related note, is it possible for VI to one day include linear
> equality constraints?
>

How are these different from just using more equations?

  Thanks,

    Matt


> 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
>> >
>> >
>>
>>
>


-- 
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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