[mlpack] MVU Bug Fix GSOC

[LI Xuran]

Hi Ryan,


>I took a quick look at your proposal and I think it is relatively clear
>and sufficiently detailed.  I am not clear on exactly what you mean by
>"5.  it might also be useful to write an algorithm to pre-process the
>dataset to make it smoother and convex"---note that the LRSDP algorithm
>breaks the convexity of SDPs and it is a nonconvex optimization.


Thanks a lot for the feedback! Yeah, you are right about the LRSDP is a nonconvex optimization, what I intend to say is that during the process of sample generation, it might be helpful if we can have some constraints (say convex and closed? I am not too sure about the detail constraints yet but there is a theorem in the paper of local minima specifying it )  on the data to guarantee that an optimal solution can always be reached on the sample created, both by LRSDP and a dual solver.


I 've gone through the rest of papers and Posts about LRSDP on Github during the past few days, as I am interested in what effort have been made to debug it. Do you think the following  ideas would be helpful to the debug project:

  1.  refactor the SDP class to allow detail constraints specified in input.
  2.  create variable template to specify linear/sparse/dense constraints on input or A(constraint matrix) and support evaluation of Tr(A_i * UU^T)


I didn't add these two to my proposal, but if you think implementing those would be useful than I can also look into it and take it as a part of the project. Maybe I can try to approach it during the community bound.

Thanks again and Best Regards.
Daniel Li

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