Add support for quadratic constraints

[amontoison]

It could be useful to treat separately quadratic and other nonlinear constraints.
An open question is how to store all hessian of the quadratic constraints?

• List of 2D COO
• 3D COO for third order tensor (rows, cols, tubes, vals)
• ...

[dpo]

Maybe this should go to NLPModels?

[amontoison]

Yes, maybe we should also move some functions like https://github.com/JuliaSmoothOptimizers/NLPModelsJuMP.jl/blob/master/src/utils.jl#L56-L73 in NLPModels.jl.

[amontoison]

@abelsiqueira

[abelsiqueira]

Should we create a simple TripletMatrix?

[dpo]

Maybe a separate package with a COOSparseMatrix type that conforms to the Julia AbstractMatrix API.

[abelsiqueira]

Agreed

[amontoison]

If we want to add support for quadratic constraints (amontoison@378439f), we need to:

• store all hessian of the quadratic constraints;
• compute nnzj of the quadratic constraints;
• separate quadratic and nonlinear constraints in NLPModels (nlin, nquad, nln).

It could be a project for a student.

[tmigot]

Simply to revitalize the debate. @amontoison
Could we consider having a COO-triplet for the matrices of the quadratic constraints, and a vector that contains the number of non-zeros elements in each matrix? For instance,

# With 2 quadratic constraints with matrices Q1 = [1, 2; 3, 4] and Q2 = [5, 6; 7, 8], we would get :
I = [1, 1, 2, 2, 1, 1, 2, 2]
J = [1, 2, 1, 2, 1, 2, 1, 2]
V = [1, 2, 3, 4, 5, 6, 7, 8]
Qnnz = [4, 8]

[dpo]

Why would they be stored together? Also they're symmetric, so we'd only store one triangle.

[tmigot]

Indeed, this is a good point that they are symmetric.
We could definitely have a list of I, J and V. This way we would avoid the Qnnz vector.

[amontoison]

I have a structure that handle a quadratic objective : https://github.com/JuliaSmoothOptimizers/NLPModelsJuMP.jl/blob/main/src/utils.jl#L47-L53

I can reuse it like this :

mutable struct QuadraticConstraint
  hessian::COO
  b::SparseVector{Float64}
  nnzh::Int
  nnzb::Int
end

and add a Vector{QuadraticConstraint} inside the model.

[dpo]

That sounds good.