Large slowdown in MOI problem construction from JuMP

[angeris]

This was prompted by #130. My current package versions are

  [1e616198] COSMO v0.7.9
  [4076af6c] JuMP v0.21.4

Here is a simple problem construction which has a sparsity structure very similar to some SDPs I'm solving:

using COSMO, SparseArrays, JuMP, LinearAlgebra, Random

Random.seed!(1234)

# Makes a subblock of size 3 w.p. ~ 98% and of size 201 otherwise
function block(i, n)
    A = spzeros(n, n)
    block_size = randn() > -2 ? 2 : 200
    A[i:min(i+block_size,n), i:min(i+block_size,n)] .= 1
    return A
end

n = 400

m = Model(COSMO.Optimizer)

A = spzeros(GenericAffExpr{Float64, VariableRef}, n, n)

@variable(m, u[1:n])

for i=1:n
    Q = block(i, n)
    for (j, k, v) ∈ zip(findnz(Q)...)
        A[j,k] = 0.0001
        add_to_expression!(A[j, k], u[i], v)
    end
end

@show nnz(A)

@constraint(m, A - sparse(I(n)) ∈ PSDCone())

@info "Finished adding constraints"

@objective(m, Min, 0)

optimize!(m)

In particular, note that the time spent "canonicalizing" the problem is rather large, even though the per-iteration cost for solving is decidedly not. I'm not sure what can be done to improve this? Perhaps a second also important question that I'm not sure about is: what's the best way of writing a standard dual form SDP in JuMP?

I will take a quick stab at profiling this, but I don't know much about COSMO.jl per se, so it's very likely I won't be particularly useful here :)

Anyways, thank you again for all of your work!