What does it mean when the parameter XPRS_MIPINFEAS takes the value -1?

Cuts can be added only from the optnode, cutmgr, and nodelpsolved callbacks (this is documented for the C api here).

Can you take a look at the examples/mosel/Solving/els.mos example shipped with Xpress? This illustrates how to add cuts from a callback (see the cb_node callback there).

Usually, what you do in a situation like this are two things:

• in the preintsol callback you check whether the solution for feasibility and reject it, if it is infeasible.
• in an optnode callback, you check whether MIPINFEAS is <=0. If so, then you check again and separate and add violated constraints, if there are any.

With this, the preintsol callback makes sure that no bad nodes are accepted, the optnode callback make sure that these solutions are actually cut off.