Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

[docs] add start_value guidance for HermitianPSDCone variables #3564

Merged
merged 1 commit into from
Nov 7, 2023
Merged

[docs] add start_value guidance for HermitianPSDCone variables #3564

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
67 changes: 66 additions & 1 deletion docs/src/manual/complex.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -67,7 +67,7 @@ julia> x = @variable(model, set = ComplexPlane())
_[1] + _[2] im
```

## Complex-valued variable bounds
## Complex-valued variable and start values bounds

Because complex-valued variables lack a total ordering, the definition of a
variable bound for a complex-valued variable is ambiguous. If you pass a real-
Expand Down Expand Up @@ -108,6 +108,26 @@ julia> start_value.(vars)
4.0
```

You can modify the bounds and start values by passing `imag(x)` or `real(x)` to
the appropriate function:

```jldoctest complex_variables
julia> set_lower_bound(imag(x), 2)

julia> lower_bound(imag(x))
2.0

julia> delete_upper_bound(real(x))

julia> has_upper_bound(real(x))
false

julia> set_start_value(imag(x), 3)

julia> start_value(imag(x))
3.0
```

## Complex-valued equality constraints

JuMP reformulates complex-valued equality constraints into two real-valued
Expand Down Expand Up @@ -251,6 +271,51 @@ julia> typeof(H[2, 1])
GenericAffExpr{ComplexF64, VariableRef}
```

### Start values

When setting the start value, you must be careful to set only the upper triangle
of real variables, and the upper triangle excluding the diagonal of imaginary
variables:
```jldoctest hermitian_psd_cone
julia> import LinearAlgebra

julia> function set_hermitian_start(
H::LinearAlgebra.Hermitian,
start::LinearAlgebra.Hermitian,
)
for j in 1:size(H, 2), i in 1:j
set_start_value(real(H[i, j]), real(start[i, j]))
if i < j
set_start_value(imag(H[i, j]), imag(start[i, j]))
end
end
return
end
set_hermitian_start (generic function with 1 method)

julia> H0 = LinearAlgebra.Hermitian(
[1 (2+3im) (5+6im); (2-3im) 4 (7+8im); (5-6im) (7-8im) 9],
)
3×3 LinearAlgebra.Hermitian{Complex{Int64}, Matrix{Complex{Int64}}}:
1+0im 2+3im 5+6im
2-3im 4+0im 7+8im
5-6im 7-8im 9+0im

julia> set_hermitian_start(H, H0)

julia> start_value.(all_variables(model))
9-element Vector{Float64}:
1.0
2.0
4.0
5.0
7.0
9.0
3.0
6.0
8.0
```

## Hermitian PSD constraints

The [`HermitianPSDCone`](@ref) can also be used in the [`@constraint`](@ref)
Expand Down
Loading