Is it possible to output the used solving algorithm?

Is the ALGORITHM attribute what you are looking for? If not, could provide a screenshot of the statistics tab you want to recreate?

Here is a snippet of Mosel code for checking the value of the ALGORITHM attribute:

case getparam("XPRS_ALGORITHM") of
  1: writeln("No LP optimization yet")
  2: writeln("Dual simplex")
  3: writeln("Primal simplex")
  4: writeln("Newton barrier or hybrid gradient")
  5: writeln("Network simplex")
  else writeln("unknown value")
end-case

Thank you both! That is what I was looking for. This leads to three more questions:

1. What does "No LP optimization yet" implies for the solution been found?
2. Does picture 1 imply show in some way how the solution is found?
3. Does picture 2 mean that there has happened LP relaxation to solve via dual simplex and what is implied by the status "unfinished"?

I accidentaly swapped the two pictures

IVE is a very old product that is no longer being maintained. Therefore it did not keep up with recent changes in the optimizer and some of the information displayed may be off. Some of the information provided in the statistics display is not read from attributes but instead collected from callback invocations throughout the solve. The "Status: Unfinished" for the LP is a bit unexpected here but may result from a very easy model that is solved already in presolve (with 0 simplex iterations).

I suggest you don't focus too much on the output of IVE for your model but instead check the relevant attributes directly. For example, the way to check the solve and solution status these days is via attributes SOLVESTATUS and SOLSTATUS.

Okay, thanks for clarification.