adding ObjectiveLimit attribute

[matbesancon]

This MR introduces an attribute to set an objective limit, after which the solver can stop.
This can be useful e.g. for separation routines, when one requires at least a certain objective value to be reached.

Setting this objective bound as a constraint in a feasibility formulation is often ill-advised and can lead to poor solver behaviour, most MIP solvers provide a dedicated parameter instead:

• Gurobi: https://www.gurobi.com/documentation/current/refman/bestobjstop.html#parameter:BestObjStop
• SCIP: limits/objectivestop is coming in the next major release
• HiGHS: objective_bound https://ergo-code.github.io/HiGHS/stable/options/definitions/#objective_bound

CPLEX seems to have this but it seems to be for LPs only?
Monotonically improving iterative solvers could also implement the attribute

[odow]

An implicit assumption is that this applies only to scalar-valued objective functions, and that the objective is Float64. What if the optimizer is BigFloat, or Rational{BigFloat}? And what about vector-valued objectives?

[matbesancon]

vetor-valued objectives is another story I wouldn't touch at first. I would be okay upgrading this to:

Union{Nothing,Real}

[odow]

Maybe we should just remove this for now. It's only implemented for a subset of attributes, and the fallback is Any.

[matbesancon]

Sure yes

[matbesancon]

good to go?

[odow]

I'm okay with this, but it probably needs @blegat to take a look.

[odow]

Bump @blegat

[odow]

Bump again @blegat

[matbesancon]

ping @joaquimg too in case

[jajhall]

• HiGHS: objective_bound https://ergo-code.github.io/HiGHS/stable/options/definitions/#objective_bound

This is applied to the dual objective in dual simplex, since it's a bound on the optimal primal objective value. So, it's not the option that should be set in the MIP context

HiGHS also has an objective_target option that was defined so that the primal simplex solver could stop if the target was reached. However this hasn't yet been implemented, and interpreting objective_target in the MIP context makes sense - and is easy to implement.

My only hesitation relates to the possibility of losing consistency with Gurobi. Its BestObjStop is just for the MIP context. Do you know whether Gurobi has a separate "target" parameter for continuous problems? My immediate search suggests not.

[matbesancon]

My only hesitation relates to the possibility of losing consistency with Gurobi. Its BestObjStop is just for the MIP context. Do you know whether Gurobi has a separate "target" parameter for continuous problems? My immediate search suggests not.

not that I have seen no, I have seen it mostly applicable on MIP (on Gurobi and CPLEX)

[matbesancon]

the attribute defined here is independent of the type of problem solved. For an LP, using objective_target makes sense for LPs, I don't know whether this should force the use of the primal simplex or throw an error if not used together with the primal simplex?

Would that be okay to have the same parameter used for MIPs?

[jajhall]

For an LP, using objective_target makes sense for LPs, I don't know whether this should force the use of the primal simplex or throw an error if not used together with the primal simplex?

Interesting thought. The default simplex strategy is to allow HiGHS to choose - and it always uses dual, since it's generally better and the implementation is better than the primal simplex implementation. I guess that it should throw an error if objective_target has been set and the user specifies dual simplex, as it feeds back useful information.

[jajhall]

Would that be okay to have the same parameter used for MIPs?

Looking at Gurobi status codes for something else yesterday, I followed the links for USER_OBJ_LIMIT, and both refer to MIP. So, it's safe to assume that LP target/bounds aren't available to users