use of tolerances

[lkapelevich]

I noticed that when passing an initial solution for a MIP, the primal_feasibility_tolerance is utilized in the feasibility check. However, only mip_feasibility_tolerance is used for checking solutions when the solver is running. I have two questions/comments:

1. This means it's possible to grab a solution out of HiGHS that is deemed feasible but when it is passed as an initial solution to the same problem, it's deemed infeasible
2. Do you know of other situations where either primal_feasibility_tolerance or dual_feasibility_tolerance values are used if solving a problem with integrality? Or, is it safe to assume that only mip_feasibility_tolerance matters?

[jajhall]

Well spotted!

Since the default value of primal_feasibility_tolerance is 1e-7, and the default value of mip_feasibility_tolerance is 1e-6, any solution that's deemed to be a feasible initial solution before calling the MIP solver will be feasible when checked within the MIP solver - unless a user modifies the tolerances so that mip_feasibility_tolerance < primal_feasibility_tolerance. I should resolve this, but it's not a priority.

1. So, yes, this is possible in theory. However, what user is going to modify the tolerances in this way?
2. No, primal_feasibility_tolerance and dual_feasibility_tolerance are not used when solving a MIP, so only mip_feasibility_tolerance matters

[lkapelevich]

Sounds good. And thanks for clarifying mip_feasibility_tolerance.

[lkapelevich]

No, primal_feasibility_tolerance and dual_feasibility_tolerance are not used when solving a MIP, so only mip_feasibility_tolerance matters

Maybe one thing just to make sure: this includes any tolerances used in pre/post processing, right?

[jajhall]

I can't say. Although there are no meaningful references to primal_feasibility_tolerance in presolve and postsolve, there are sure to be some magic numbers there.

[fwesselm]

It seems that primal_feasibility_tolerance is used in HighsPostsolveStack::DuplicateColumn::undo and related code.

For example, shouldn't mip_feasibility_tolerance (or its value) be used here if a MIP solution is postsolved?

[jajhall]

When I first looked at postsolve, I thought that the use of primal_feasibility_tolerance was just for some debugging code that I introduced, but you're right. Sometime I'll look through the use of tolerances in presolve/postsolve as it could explain some very occasional strange behaviour, but I can't prioritise it