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[docs] add warning about Y <= X, Set() syntax #3769

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Jun 9, 2024
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[docs] add warning about Y <= X, Set() syntax #3769

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[docs] add warning about Y <= X, Set() syntax
odow Jun 5, 2024
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odow Jun 5, 2024
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18 changes: 13 additions & 5 deletions docs/src/manual/constraints.md
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Expand Up @@ -1238,8 +1238,9 @@ julia> @constraint(model, x in MOI.ExponentialCone())
## Set inequality syntax

For modeling convenience, the syntax `@constraint(model, x >= y, Set())` is
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Note that as per https://docs.julialang.org/en/v1/manual/unicode-input/
⪰ can be "trivially" inputted as \succeq.

Wouldn't it be possible to:

@constraint(model, x \succeq y)
# error: specify one of the conic sets

@constraint(model, x >= y, <... Some conic set ...>)
# warning: use \succeq instead

@constraint(model, x \succeq y, <... Some non-conic set ...>)
# warning: use >= instead

@constraint(model, x >= y)
# becomes @constraint(model, x - y, Nonnegatives)

@constraint(model, x <= y)
# becomes @constraint(model, x - y, Nonpositives)

Is the concern that someone writes @constraint(model, x >= y) thinking it means PSDCone,
it silently works, and doesn't do what's expected? Or is there some other concern?

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Is the concern that someone writes @constraint(model, x >= y) thinking it means PSDCone,
it silently works, and doesn't do what's expected?

Yes.

We won't be adding support for \succeq. There is too much risk of confusion.

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:/ I really feel such a decision should be made with a larger headcount than i see here.

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I'll open a new issue

short-hand for `@constraint(model, x - y in Set())`. Therefore, the following
calls are equivalent:
short-hand for `@constraint(model, x - y in Set())`.

Therefore, the following calls are equivalent:
```jldoctest set_inequality
julia> model = Model();

Expand All @@ -1250,9 +1251,6 @@ julia> y = [0.5, 0.75];
julia> @constraint(model, x >= y, MOI.Nonnegatives(2))
[x[1] - 0.5, x[2] - 0.75] ∈ MathOptInterface.Nonnegatives(2)

julia> @constraint(model, y <= x, MOI.Nonnegatives(2))
[x[1] - 0.5, x[2] - 0.75] ∈ MathOptInterface.Nonnegatives(2)

julia> @constraint(model, x - y in MOI.Nonnegatives(2))
[x[1] - 0.5, x[2] - 0.75] ∈ MathOptInterface.Nonnegatives(2)
```
Expand All @@ -1270,6 +1268,11 @@ julia> @constraint(model, x .- 1 >= 0, MOI.Nonnegatives(2))
[x[1] - 1, x[2] - 1] ∈ MathOptInterface.Nonnegatives(2)
```

!!! warning
The syntax `@constraint(model, y <= x, Set())` is supported, but it is not
recommended because the value of the primal and dual solutions associated
with the constraint may be the negative of what you expect.

## Second-order cone constraints

A [`SecondOrderCone`](@ref) constrains the variables `t` and `x` to the set:
Expand Down Expand Up @@ -1440,6 +1443,11 @@ julia> @constraint(model, X >= Y, PSDCone())
X[2,1] - 2 X[2,2] - 1] ∈ PSDCone()
```

!!! warning
The syntax `@constraint(model, Y <= X, PSDCone())` is supported, but it is
not recommended because the value of the primal and dual solutions associated
with the constraint may be the negative of what you expect.

### Symmetry

Solvers supporting PSD constraints usually expect to be given a matrix that
Expand Down
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