Indicator constraint support for complex-valued equality constraints

[wickyw]

Dear all,

Recently, I found out that JuMP supports complex-valued equality constraints (which made me very happy, since that makes my models read a lot nicer!). The manual states the following:

JuMP reformulates complex-valued equality constraints into two real-valued constraints: one representing the real part, and one representing the imaginary part. Thus, complex-valued equality constraints can be solved any solver that supports the real-valued constraint type.

However, it does not seem to reformulate indicator constraints with complex-valued equality constraints in them. A mininum working example:

using JuMP, HiGHS

model = Model(HiGHS.Optimizer)

@variable(model, x, Bin)
@variable(model, y in ComplexPlane(), lower_bound=-1.0 + im*-1.0, upper_bound=1.0 + im*1.0)
@constraint(model, x --> {y == 0})

@objective(model, Max, real(y))
optimize!(model)

Output:
ERROR: Constraints of type MathOptInterface.VectorAffineFunction{ComplexF64}-in-MathOptInterface.Indicator{MathOptInterface.ACTIVATE_ON_ONE, MathOptInterface.EqualTo{ComplexF64}} are not supported by the solver.

Of course, the equivalent "noncomplex" indicator constraint does work:

using JuMP, HiGHS

model = Model(HiGHS.Optimizer)

@variable(model, x, Bin)
@variable(model, y in ComplexPlane(), lower_bound=-1.0 + im*-1.0, upper_bound=1.0 + im*1.0)

# @constraint(model, x --> {y == 0})
@constraint(model, x --> {real(y) == 0})
@constraint(model, x --> {imag(y) == 0})

@objective(model, Max, real(y))
optimize!(model)

Would it be possible to have JuMP interpret the former as the latter?

[wickyw]

If you could give me some pointers, I'd also be open to writing a patch myself. However, this would be my first contribution, so I might need some guidance ;).

[odow]

I've transferred this to MathOptInterface. It's something we can fix, but it is too difficult for a first contribution.

[odow]

I have this working in #2921

julia> using JuMP, HiGHS

julia> begin
           model = Model(HiGHS.Optimizer)
           set_silent(model)
           @variable(model, x, Bin)
           @variable(model, y in ComplexPlane(), lower_bound=-1.0 + im*-1.0, upper_bound=1.0 + im*1.0)
           @constraint(model, x --> {y == 0})
           @objective(model, Max, real(y))
           optimize!(model)
           value(x), value(y)
       end
(0.0, 1.0 + 1.0im)

[wickyw]

Wow, that's really quick, thank you! I've tested it and found it working also on a more complicated example.

Looking at the code, that indeed would've been too much for a first contribution ;).

Thanks a lot!