`MultirowChange` overwrites other constraints

[mtanneau]

import Gurobi
import MathOptInterface
MOI = MathOptInterface

m = Gurobi.Optimizer()

x = MOI.add_variable(m)

# Create two linear constraints, wrapped in a single VectorAffineFunction constraint
n = 2
c1 = MOI.add_constraint(m,
    MOI.ScalarAffineFunction([MOI.ScalarAffineTerm(2.0, x)], 0.0),
    MOI.EqualTo(0.0)
)
# Add another linear constraint
c2 = MOI.add_constraint(m,
    MOI.VectorAffineFunction(
        [MOI.VectorAffineTerm(i, MOI.ScalarAffineTerm(1.0, x)) for i in 1:n],
        zeros(n)
    ), MOI.Zeros(n)
)

# Now create another variable
y = MOI.add_variable(m)

# Multi-row change
# That Multirow should raise an error, because the output dimension of c1 is 2
MOI.modify(m, c2, MOI.MultirowChange(y, [(1, 1.1), (2, 2.2), (3, 3.3)]))

# The above call did not raise an error, and modified c1
MOI.get(m, MOI.ConstraintFunction(), c1)

outputs

MathOptInterface.ScalarAffineFunction{Float64}(MathOptInterface.ScalarAffineTerm{Float64}[ScalarAffineTerm{Float64}(2.0, VariableIndex(1)), ScalarAffineTerm{Float64}(1.1, VariableIndex(2))], 0.0)

It appears that MOI.modify with a MultirowChange ends up calling LQOI.change_matrix_coefficient!, which simply re-writes matrix coefficients without any checks. In particular:

• Other constraints can be over-written (cf example above)
• Instead of changing coeff of variable j of the i-th output dimension of the vector-valued constraint, it changes coeff (i, j) of the whole problem's constraint matrix.

[odow]

I don't think multirow change has been utilised, so there are probably lots of bugs like this.

Note that the Gurobi wrapper is being re-written (https://github.com/JuliaOpt/Gurobi.jl/pull/216), and it doesn't implement MultirowChange because it doesn't support VectorAffineFunctions.

The most helpful thing would be to add lots of tests to moi hitting various edge cases.

[blegat]

Because Gurobi does not support VectorAffineFunctions, MultirowChanges will be transformed into ScalarCoefficientChange here: https://github.com/JuliaOpt/MathOptInterface.jl/blob/ef83d2381b2e26a3e6466b8bc34b6687c7c20c61/src/Bridges/Constraint/scalarize.jl#L89-L96