[mlpack] MVU Bug Fix GSOC

[LI Xuran]

Hey Ryan,


Just an update on what I 've done with the project over the weekend.

I watched some videos on youtube about how to decide whether a solution is a saddle point in a multivariable function...but it would take some hard work to generalize that method to nonlinear case.


I've gone over the codebase of methods/mvu and optimizer over the weekend. I find the template initialization a bit confusing with lots of <<<>>> but the other parts are mostly fine. I will need to spend some time matching the algorithm suggested in the paper with the actual code we have but this shouldn't be hard.

And currently I don't think any further constraints to the SDP class are needed.


Best Regards

Daniel Li

________________________________
From: Ryan Curtin <ryan at ratml.org>
Sent: 04 April 2018 20:53:52
To: LI Xuran
Cc: mlpack at lists.mlpack.org
Subject: Re: [mlpack] MVU Bug Fix GSOC

On Wed, Apr 04, 2018 at 10:01:11AM +0000, LI Xuran wrote:
> Hey Ryan,
>
> Sorry for the ambiguity. Basically what  I did was just a shortlist of
> the major past topics related to LRSDP on Github. I didn't realise
> that the sparse and dense constraint is already implemented, which is
> great.
>
> By "detail constraints" I basically want to say is that it would be
> helpful to have some dataset that is guaranteed to not have any saddle
> point, i.e. having only local and global minima so that we can check
> the convergence of the LRSDP on problems not involving saddle point.
> Maybe it shouldn't be implemented as  a constraint but just as
> something to keep in mind during the generation of the data.
>
> since sparse and dense constraints have already been implemented in
> MUV SDP then yeah I think a variadic template wouldn't be quite of
> help in this case. I haven't give much thought to this over the past
> few days as I was caught up with coursework and hackathon, but I will
> look further into the code base and give a detailed suggestion on
> whether it is possible to further constraint the question or pass on
> some useful information to the SDP class this week.

Hi Daniel,

I hope the hackathon was enjoyable.  Thanks for the clarifications here,
I think I understand better now.  I think it may be difficult to devise
an LRSDP problem that has no saddle points (and prove that it has no
saddle points).

Thanks,

Ryan

--
Ryan Curtin    | "Bye-bye, goofy woman.  I enjoyed repeatedly
ryan at ratml.org | throwing you to the ground." - Ben Jabituya
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