Question about tolerances

[fontanf]

Hi,

Highs provides multiple tolerance options: kkt_tolerance, primal_feasibility_tolerance, dual_feasibility_tolerance etc
https://ergo-code.github.io/HiGHS/dev/options/definitions/

When solving an LP, are these tolerances used on the user model or on the presolved model?

[jajhall]

Both, in particular when assessing feasibility and optimality for the original model.

[fontanf]

Thank you for the quick answer. How is it implemented? Is the tolerance check performed on the solution of the presolved model, and if the checks pass, then the solution is converted to the user model and checked again? Could you point me to where this is implemented in the code?

[jajhall]

Do you want the story for LP or MIP?

[fontanf]

For LP, in particular with the simplex algorithm

[jajhall]

That's a simple case. The presolved LP is solved to the tolerances and then postsolve is applied to the primal and dual solutions, and basis. The original problem is then solved to the tolerances from the resulting basis. Typically no simplex iterations are required

[fontanf]

Thanks, and thank you for the quick replies