Better error messages for vector variable bounds

[pierre-haessig]

Hello,

As suggested by @odow in this discussion, I report a possible enhancement of error message when one inadvertidly uses broadcasted vector bounds when creating a vector of JuMP variables.

Considering the following preamble code,

using JuMP
model = Model()
xmax = [10., 0.]

the correct way to have a variable x<=xmax elementwise is by using an explicit indexing variable (which is documented, but not exactly for this vector slicing usecase)

@variable(model, x[i=1:2] <= xmax[i])

However, there is a wrong approach that someone can easily follow (at least I did -;)), using broadcasting on the comparison operator:

@variable(model, x[1:2] .<= xmax)

which yields the surprising error message:

ERROR: LoadError: In `@variable(model, x[1:2] .<= xmax)`: Unknown sense .<=.

Also, in the case of two bounds, with the same mistake:

@variable(model, 0 <= x[1:2] .<= xmax)

the error message is different but also not helpful:

ERROR: LoadError: In `@variable(model, 0 <= x[1:2] .<= xmax)`: Use the form lb <= ... <= ub.

Expected behavior: in an ideal world, the error message would point out to the correct solution (ex : "broadcasted constraints are not yet supported, use ... instead"). Alternatively, it may be worth supporting the broadcasted syntax, but I don't have enough background on JuMP to judge the difficulty of the task. This last idea may relate to the closed issue #1455, although it was about applying broadcasting on the set_lower_bound function not within the @variable macro.

[odow]

We should endeavor to make this work:

@variable(model, x[1:2] .<= xmax)