When possible, ensure basis and internal solution are propagated when model status is `HighsModelStatus::kUnknown`

[deryaozyurt]

Greetings, The attached (probably degenerate) problem gives the following output with status "Unknown" (perhaps similar to issue #2015):

Coefficient [ranges:] Matrix [1e+00, 1e+00] Cost [1e-02, 2e+03] Bound [7e-03, 7e+04] RHS [2e+04, 3e+04] Presolving model 144 rows, 8041 cols, 8327 nonzeros 0s 144 rows, 7872 cols, 8158 nonzeros 0s Presolve : Reductions: rows 144(-0); columns 7872(-1152); elements 8158(-1152) Solving the presolved LP Using EKK dual simplex solver - serial Iteration Objective Infeasibilities num(sum) 0 6.5170028673e-02 Pr: 50(1.02587e+06) 0s 362 2.4550484492e+07 Pr: 0(0); Du: 1(1.3e-07) 0s 362 2.4550484492e+07 Pr: 0(0); Du: 1(1.3e-07) 0s Model status : Unknown Simplex iterations: 362 Objective value : 2.4550484492e+07 HiGHS run time : 0.12 degenerateProblem.zip

[jajhall]

Yes, this is the anti-cycling test causing termination of the simplex solver with a dual infeasibility. Since that dual infeasibility is 1.3e-7, it's fair for a user to assume that the problem has been solved.

That said, when I used HiGHS to write out the solution, there was no basis, and there appeared to be primal infeasibilities. It looks as if something is "not done" when the problem status is "Unknown". That's something to be addressed, as is logging to inform the user why the solution status is "Unknown" (see #1979), and how to assess whether it's close enough to be optimal.