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I believe there may be an issue here:
MathOptInterface.jl/src/Test/test_nonlinear.jl
Lines 1391 to 1400 in 2401296
The interval on each x should be Interval(2.001, 9.999) instead of Interval(-2.001, 9.999) for log(x - 2) to be defined.
Here's an example using Ipopt,
using JuMP, Ipopt
model = Model(Ipopt.Optimizer);
@variable(model, -2.001 <= x[1:10] <= 9.999);
f = log(x[1] - 2)^2 + log(10 - x[1])^2;
for i = 2:10
f += log(x[i] - 2)^2 + log(10 - x[i])^2
end
f -= (x[1] * x[2] * x[3] * x[4] * x[5] * x[6] * x[7] * x[8] * x[9] * x[10])^0.2;
@objective(model, Min, f);
JuMP.optimize!(model)which returns EXIT: Invalid number in NLP function or derivative detected.
If the variables are defined as @variable(model, 2.001 <= x[1:10] <= 9.999) instead, then the solution is found.
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