[petsc-dev] Discussion about time-dependent optimization moved from PR

[Barry Smith]

> On Oct 15, 2017, at 10:14 AM, Matthew Knepley <knepley at gmail.com> wrote:
> 
> Someone had to do it.
> 
> I will not try to frame the entire discussion. Barry has already thrown down the "show me your interface" gauntlet. However, I want to emphasize one point that may have been lost in the prior discussion. Every example I have looked at so far is focused on the reduced space formulation of the optimization problem. However, I am interested in the full space formulation so that I can do multigrid on the entire optimal control problem. This is not a new idea, in particular Borzi does this in SIAM Review in 2009. I think we have a tremendous opportunity here since other codes cannot do this, it has the potential (I think) for much better globalization, and perhaps can be faster.
> 
> So, when we come up with interface proposals, I think we should keep a full space solution method in mind.

    Matt,

    Thanks for bringing this topic up.

   Yes, if it could be a command line option to get it that would be optimal. If not how close can we get to that? I still don't understand all the relationships between the 

     reduced space formulation (adjoints) 


     full space (parallel in time) 

approaches. Do they sometimes?/always?/rarely? represent the exact same model and discretization? Seemingly not, as how can the "full space" support adaptive time-stepping and mesh refinement/unrefinement (while that is easy with continuous adjoints and doable on the forward ODE solve for discrete (though solving the adjoint in the discrete case means using the same meshes and time steps as the forward ODE solve)).

  Barry

   
> 
>   Thanks,
> 
>      Matt
> 
> -- 
> 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
> 
> https://www.cse.buffalo.edu/~knepley/