SDPA-GMP

[Mark L. Stone]

Has any consideration been made to making SDPA-GMP , which uses GNU Multiple Precision, available under YALMIP? Would it be a monumental effort to make that work under YALMIP? I'm sure it will be slow, but if you really need the accuracy, say on an intrinsically very ill-conditioned problem ...

Per http://www.optimization-online.org/DB_FILE/2010/01/2531.pdf from January 2010, there is (was?) an online SDPA solver http://sdpa.indsys.chuo-u.ac.jp/portal/ which includes (included) SDPA-GMP, but my connection timed out trying to reach the site.

I don't have any current SDPs for which higher than double precision seems necessary, but perhaps some day I might, and perhaps other people do.

[Johan Löfberg]

I think you asked this last year or so in an email to the developers of sdpa, with me on cc, and I think the answer was that it would be very hard to connect it to matlab

[Johan Löfberg]

Could not find that mail, so I am mistaken. I do however remember a discussion with someone + sdpa developers with the conclusion above

[Mark L. Stone]

Yes, I have my senior moments, but I have no recollection of having previously inquired about this. Anyhow, you'll note that I speculated it might be a monumental effort.

If it could be connected to MATLAB, would it be difficult to make available under YALMIP, or does that depend on how the MATLA implementation is done?

[Johan Löfberg]

If available in matlab with an interface similar to all other interfaces, I don't see why there would be any problems (assuming computations are done in quad, but data/solutions are double)

[Mark L. Stone]

Quad, ha ha, we're already in SW computation anyway, so might as well think big. No need to restrict attention to quad once we've decided to forego HW DP. 

Octuple or bust.  That's about what it takes me to get a single digit of accuracy in adaptive Gaussian Process calculations (conditional Normal, essentially Schur complement for conditional covariance calculation, and similar for conditional mean) calculations on extremely ill-conditioned covariance matrices, used to simulate simulations for a test mode of my stochastic optimizer, and at least twice as many digits if using finite differences which make the ill-conditioning even greater.by placing many points very close together, while others are at different scales - not really an optimization problem (although could be cast as one), but perhaps similar to the kind of ill-conditioning which can occur on real optimization problems, and which is intrinsic to the problem.

[Johan Löfberg]

https://github.com/giofantuzzi/mpYALMIP

[Mark L. Stone]

Excellent. Although it looks like I'll have to resurrect my decrepit LINUX installation in order to use it.

[Mark L. Stone]

I made inquiry at https://github.com/giofantuzzi/mpYALMIP/issues as to
1) whether there are any plans for a WINDOWS version
2) any thought of modifying SDPA-GMP to use arbitrary precision outward rounded interval or radial arithmetic

[Mark L. Stone]

mpYALMIP-neos has been produced as a fork from mpYALMIP, which, it it works correctly, will allow sdpa-gmp to be used under YALMIP on WINDOWS by running the solver on NEOS.  See https://github.com/htadashi/mpYALMIP-neos .

As I just reported at https://github.com/giofantuzzi/mpYALMIP/issues/1#issuecomment-283767954 , this did not work correctly when I tried it, even though YALMIP reported

info: 'Successfully solved (SDPA-GMP-NEOS)'
problem: 0

I will leave it to Johan and the sdpa-gmp-neos and sdpa-gmp developers to get to the bottom of it.  Thanks.