Solving nonconvex problems using Gurobi

Specific Domains Optimization (Mathematical)
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1

I just wanted to confirm if this is the right way to solve a nonconvex problem with bilinear terms (continuous times continuous variables) using Gurobi. I assumed to define a nonlinear constraint or objective, I should be using @NLconstraint; however, I get the following error:
ERROR: The solver does not support nonlinear problems (i.e., NLobjective and NLconstraint).

So, basically the following problem throws the error:

using JuMP, Gurobi

model = Model(Gurobi.Optimizer)
set_optimizer_attribute(model, "NonConvex", 2)

@variable(model, x >= 0)
@variable(model, 0 <= y <= 10)
@NLconstraint(model, x*y <= 10)
@NLobjective(model, Max, x*y-3*x+2*y)

optimize!(model)

However, the following model works fine:

using JuMP, Gurobi

model = Model(Gurobi.Optimizer)
set_optimizer_attribute(model, "NonConvex", 2)

@variable(model, x >= 0)
@variable(model, 0 <= y <= 10)
@constraint(model, x*y <= 10)
@objective(model, Max, x*y-3*x+2*y)

optimize!(model)

So, I suppose if I am trying to solve a nonlinear problem with Gurobi I am fine with using @constraint instead of @NLconstraint even if the expression has nonlinear terms?

2

Gurobi supports quadratic constraints as well as linear, and JuMP’s @constraint works for both. So this is fine.

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