Is it possible to allow a range for |Aeq*x-beq|<10e-6 in intlinprog function?

Good morning, everyone,

In MATLAB's intlinprog function, is it possible to specify a tolerance for the equality constraints such that the solution satisfies ∣Aeq⋅x−beq∣ <10−6 rather than requiring exact equality? In other words, can I define a tolerance range for the equality constraints to allow for small numerical deviations, and if so, how can this be configured within the solver settings?

I'm working with a model where strict equality sometimes leads to infeasibility due to rounding or numerical issues, so I’d like to relax the constraint slightly while still maintaining high accuracy.

Thanks.

Benson

Answer 1

[Torsten]

Which vector norm for the inequality ∣Aeq⋅x−beq∣ <10−6 do you have in mind ?

Aeq*x - beq <= 1e-6
Aeq*x - beq >= -1e-6

would define your constraint elementwise.

Answer 2

[Matt J]

is it possible to specify a tolerance for the equality constraints such that the solution satisfies ∣Aeq⋅x−beq∣ <10−6 rather than requiring exact equality

Not only is it possible, it is always done.The ConstraintTolerance optimoptions parameter sets the tolerance on both the equality and inequality constraints,

https://www.mathworks.com/help/optim/ug/intlinprog.html#btv2x05