[Bridges] add {SOS1,SOS2,Indicator}ToMILPBridge

[odow]

Part of #2316

I'll need to run the solver-tests, because this should let HiGHS support SOS constraints, but it will probably also start supporting Indicator because of IndicatorToSOS, except that IndicatorToSOS introduces an unbounded variable in the SOS.

https://github.com/jump-dev/MathOptInterface.jl/actions/runs/6620504066

[odow]

So this is pretty breaking (to tests, not in practice) because it opens up IndicatorToSOS1 bridge. So I think we need to add an IndicatorToMILPBridge to fix it.

[odow]

https://github.com/jump-dev/MathOptInterface.jl/actions/runs/6634509879

[odow]

Found a few bugs in jump-dev/HiGHS.jl#187, jump-dev/HiGHS.jl#188.

[odow]

https://github.com/jump-dev/MathOptInterface.jl/actions/runs/6647030587

[odow]

https://github.com/jump-dev/MathOptInterface.jl/actions/runs/6647326291

[odow]

Failures are:

• COSMO: test_attribute_TimeLimitSec
• EAGO: test_attribute_TimeLimitSec, and some out-of-bound accesses?
• Pavito: test_linear_Indicator_constant_term because not canonicalized? [Test] allow skipping ScalarFunctionConstantNotZero errors #2325
• ProxSDP: test_attribute_TimeLimitSec
• SCIP: bug in SCIP checking is_valid Fix is_valid for ZeroOne and Integer constraints in MOI wrapper scipopt/SCIP.jl#277

[odow]

https://github.com/jump-dev/MathOptInterface.jl/actions/runs/6659265716

[odow]

It's pretty cool that stuff like this works now:

using JuMP, HiGHS
xp = 0.0:0.1:pi
yp = sin.(xp)
n = length(xp)
model = Model(HiGHS.Optimizer)
@variable(model, 0 <= x <= π)
@variable(model, -1 <= y <= 1)
@variable(model, 0 <= λ[1:n] <= 1)
@variable(model, z, Bin)
@constraint(model, λ in SOS2())
@constraint(model, sum(λ) == 1)
@constraint(model, xp' * λ == x)
@constraint(model, yp' * λ == y)
@constraint(model, z --> {x <= 0.45})
@constraint(model, !z --> {x == y})
@objective(model, Max, x)
optimize!(model)

This will let us use SOS1 and SOS2 and indicator constraints in the documentation tutorials.

[blegat]

Yes, it's also helpful for teaching since then you can add complexity incrementally. The students can use indicator constraints without having learned the big-M formulation as requirement.