I’m not sure where to put this as it’s not specifically an issue, and I’m not sure who would improve it.

For my research I need to solve a bilinear model and I’d like to use an open-source solver ideally.

## Rough example of my constraints

My constraint is like xy==0. I relax this using big_M to roughly

```
@variable(model, 0 <= x[1:n])
@variable(model, y[1:n] <= 0)
@variable(model, 0 <= u[1:n] <= 1, binary=true)
@constraint(model, big_m_x, x .≤ 10 .* (1 .- u))
@constraint(model, big_m_y, -10 .* u .≤ y)
```

I’ve formulated a MWE example (see below), in this scenario Gurobi solves the problem in 0.4s while HiGHS takes 40-60 seconds which is >100 times slower. As my actual problem is much bigger than the example below HiGHs become prohibitively slow.

I appreciate Gurobi is often quicker than HiGHS, but not usually by this much, it seems like my HiGHs implementation is missing a trick?

## MWE

Note I haven’t gone through this MWE thoroughly, it just serves to demonstrate the timing scenario and is roughly similar to my actual problem

```
using JuMP, HiGHS, Gurobi
function create_model(n, nl, solver)
if solver==:H
model = Model(HiGHS.Optimizer)
elseif solver==:G
model = Model(Gurobi.Optimizer)
end
if nl
@variable(model, 0 <= x[1:n] <= 10)
@variable(model, -10 <= y[1:n] <= 0)
@constraint(model, [i=1:n], x[i]*y[i] ==0)
else
@variable(model, 0 <= x[1:n])
@variable(model, y[1:n] <= 0)
@variable(model, 0 <= u[1:n] <= 1, binary=true)
@constraint(model, big_m_x, x .≤ 10 .* (1 .- u))
@constraint(model, big_m_y, -10 .* u .≤ y)
end
@objective(model, Min, sum(x[i] + -2*y[i] for i in 1:n))
@constraint(model, [i=1:n], x[i] - y[i] >= 1)
@constraint(model, [i=1:n], x[i] - y[i] <= 15)
return model
end
n = 100_000
model = create_model(n,false,:G)
optimize!(model)
# Gurobi = 0.4
# HiGHS = 58.6
solve_time(model)
objective_value(model)
sum(value.(model[:x]))
sum(value.(model[:y]))
```

with

```
(jl_MPgoHK) pkg> st
Status `/private/var/folders/63/lgx7112n3b58qj9r923y2v680000gp/T/jl_MPgoHK/Project.toml`
[2e9cd046] Gurobi v1.2.3
[87dc4568] HiGHS v1.9.0
[4076af6c] JuMP v1.22.1
```