Termination callback

[odow]

I'm working on MathOptIIS, and I have a use-case:

• I want to terminate the solver if more than 10 seconds have passed AND it has a primal feasible solution.

I think we could fire this: every time we have a feasible primal solution and return a Bool indicating whether to terminate.

There's support for this in Gurobi, HiGHS, Ipopt, etc.

There's an open question on whether we should allow accessing the current best primal/dual bound.

I've seen a few similar questions on the forum over the years:

• https://discourse.julialang.org/t/using-optimizer-callbacks-within-jump-to-terminate-mip-solve/46679?u=odow
• https://discourse.julialang.org/t/solver-specific-callback-for-custom-termination-rule-for-lp-barrier-using-gurobi-and-jump/104391 (Barrier is hard. Maybe we just assert for MIPs)
• https://discourse.julialang.org/t/set-ipot-with-jump-to-terminate-only-if-max-time-is-reached/72160 (fixed in Ipopt, but hints at a more general question)

[odow]

Here's another case:

• I have a non-convex nonlinear approximation of some bilinear term. I want to get a feasible solution, then use it to warm-start the solve of the NLP equivalent and compare objective values.