I added 1 Million constraints to an LP unwittingly

Specific Domains Optimization (Mathematical)
, , , ,
7

Here is one more question. I have 2 vectors: r, c and one asymmetric matrix X.
r is a 101-element SparseArrays.SparseVector{Float64, Int64} with 101 stored entries:
c is a 170-element SparseArrays.SparseVector{Float64, Int64} with 3 stored entries:
X is a 101×170 Matrix{JuMP.AffExpr}:
I now need to write the constraint @constraint(model, r' * X * c >= 0),
Which style should I choose, to maximize the performance (assume I need to add 1 million of this type of constraint, assume 101 and 170 both increase)

  1. @constraint(model, transpose(r) * X * c >= 0)
  2. @constraint(model, transpose(r) * (X * c) >= 0)
  3. @constraint(model, dot(r, X, c) >= 0)
  4. @constraint(model, tr(c * transpose(r) * X) >= 0)
  5. @constraint(model, sm(r * transpose(c), X) >= 0), where sm is here.
  6. should I use transpose() or ' (adjoint)?

And this list can be enlarged because there are many equivalent forms.