Errors during SDP optimization with "M2" solver

[LegionMammal978]

Calling optimize() with an SDP problem from the SemidefiniteProgramming package can throw errors even when the instance is well-formed and feasible. For instance, the script:

loadPackage "SemidefiniteProgramming";
optimize(sdp(matrix{{0, 0}, {0, 1}}, 1:matrix{{1, 0}, {0, 0}}, matrix{{1}}), Solver=>"M2");

throws the error:

/usr/share/Macaulay2/Core/robust.m2:101:30:(1):[22]: error: no method for binary operator * applied to objects:
            null (of class Nothing)
      *     | 1 0 | (of class Matrix)
            | 0 0 |
/usr/share/Macaulay2/SemidefiniteProgramming.m2:531:48:(2):[21]: --back trace--
/usr/share/Macaulay2/Core/lists.m2:326:62:(1):[20]: --back trace--
/usr/share/Macaulay2/Core/lists.m2:326:49:(1):[19]: --back trace--
/usr/share/Macaulay2/Core/lists.m2:326:32:(1):[18]: --back trace--
/usr/share/Macaulay2/Core/matrix1.m2:30:18:(1):[17]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:154:98:(1):[15]: --back trace--
/usr/share/Macaulay2/Core/option.m2:17:14:(1):[14]: --back trace--
/usr/share/Macaulay2/SemidefiniteProgramming.m2:531:20:(2):[13]: --back trace--
/usr/share/Macaulay2/Core/option.m2:17:14:(1):[12]: --back trace--
/usr/share/Macaulay2/SemidefiniteProgramming.m2:494:42:(2):[11]: --back trace--
/usr/share/Macaulay2/Core/option.m2:17:14:(1):[10]: --back trace--
/usr/share/Macaulay2/SemidefiniteProgramming.m2:392:37:(2):[9]: --back trace--
/usr/share/Macaulay2/Core/methods.m2:154:98:(1):[8]: --back trace--
example.m2:2:8:(3):[6]: --back trace--
/usr/share/Macaulay2/Core/startup.m2:65:23:(0):[6]: --back trace--
/usr/share/Macaulay2/Core/Core.m2:131:28:(1):[5]: --back trace--
/usr/share/Macaulay2/Core/Core.m2:127:13:(1):[3]: --back trace--
/usr/share/Macaulay2/Core/Core.m2:138:29:(1):[2]: --back trace--
/usr/share/Macaulay2/Core/startup.m2:533:66:(0):[1]: --back trace--
/usr/share/Macaulay2/Core/startup.m2:623:30:(0): --back trace--

I ran into this error while trying to use the lowerBound() function from the SumsOfSquares package, which internally constructs a similar instance:

loadPackage "SumsOfSquares";
QQ[x];
lowerBound(x^2, RoundTol=>infinity, Solver=>"M2");

This is with M2 version 1.25.11 from ppa:macaulay2/macaulay2 on Ubuntu 24.04.

EDIT: I've added the Solver=>"M2" option to the example inputs for better reproducibility.

[LegionMammal978]

Actually, this might be a packaging issue, since Macaulay2Web (with M2 version 1.25.11-1572-g6198e3f03b-dirty (vanilla)) seems to run both programs without issue.

[d-torrance]

I'm running essentially the same system as you (Ubuntu 24.04, but a snapshot of the development branch rather than the 1.25.11 release, but there haven't been any big changes that would affect this, I don't think...) and I'm not able to reproduce the problem.

That being said, we have run into some strange SDP issues before thanks to things like sorting keys in hash tables and floating point errors. See, e.g., #1579

[LegionMammal978]

I think I've spotted the discrepancy: by default, when installing macaulay2 from ppa:macaulay2/macaulay2, coinor-csdp is included as a recommended package, so the "CSDP" solver is used by default. But I wanted to save on the ~636 MB worth of recommended packages, so I installed it as sudo apt install macaulay2 --no-install-recommends, which ends up using the built-in "M2" solver by default. I can reproduce the issue on Macaulay2Web by explicitly asking for the "M2" solver:

loadPackage "SemidefiniteProgramming";
optimize(sdp(matrix{{0, 0}, {0, 1}}, 1:matrix{{1, 0}, {0, 0}}, matrix{{1}}), Solver=>"M2");

In the meantime, I'll just make sure to install CSDP and use that for my program.

[d-torrance]

This is kind of fixed in #4105. There's no more error, but the SDP fails:

i1 : needsPackage "SemidefiniteProgramming";

i2 : optimize(sdp(matrix{{0, 0}, {0, 1}}, 1:matrix{{1, 0}, {0, 0}}, matrix{{1}}), Solver=>"M2")

o2 = (, , , SDP failed)

o2 : Sequence