Add some realistic tests for sdpb

[davidsd]

One possibility is "SingletScalarAllowed_test_nmax6" from https://gitlab.com/davidsd/scalars-3d/-/blob/master/src/Projects/Scalars3d/SingletScalar2020.hs . Perhaps we want to do it at lower nmax. If we change Bound.remoteCompute to Bound.remoteComputeKeepFiles, then we can grab the json files it outputs and use them.

• [x] #103
• [x] #104
• [ ] #105
• [ ] Other tests suites (see links below)

[davidsd]

Vasiliy found this suite of SDP tests https://github.com/vsdp/SDPLIB . The primal form of these problems takes exactly the form of a PMP with constant matrices. So we can run these tests.

[vasdommes]

Some SDP test/benchmark references from https://link.springer.com/article/10.1007/s10107-006-0029-9, chapter 5):

• https://github.com/vsdp/SDPLIB (SDPA format)
• TRUSS collection Available at http://www2.am.uni-erlangen.de/∼kocvara/pennon/problems.html (invalid link). Working link (probably the same): https://web.mat.bham.ac.uk/kocvara/pennon/problems.html
• Mittelmann, H.: Benchmarks for Optimization Software; as of 26 November 2005. Available at https://plato.asu.edu/bench.html. Visualization: https://mattmilten.github.io/mittelmann-plots/
• Toh, K.C.: Solving large scale semidefinite programs via an iterative solver on the augmented systems. SIAM J. Optim. 14, 670–698 (2003) https://optimization-online.org/wp-content/uploads/2003/01/596.pdf

[vasdommes]

Currently we have a simple (1x1 block) test for pvm2sdp and sdpb. We also have a non-trivial test for sdp2input, but its result is not solvable by sdpb, see #38 We should replace the sdp2input test with something small but 'realistic'.