Gurobi and non linear

Specific Domains Optimization (Mathematical)
6 
using JuMP, Gurobi

N = 2
column(x::VariableRef) = Gurobi.c_column(backend(owner_model(x)), index(x))
model = direct_model(Gurobi.Optimizer())
@variable(model, x[i in 1:N])
@variable(model, y[i in 1:N])
for i in 1:N
    GRBaddgenconstrPow(backend(model), "x$i^0.5", column(x[i]), column(y[i]), 0.5, "")
end
@constraint(model, sum(y) <= k)
@objective(model, Min, k) # something 
optimize!(model)
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