Gradient not zero when optimizing function

Specific Domains Optimization (Mathematical)
1

I am optimizing a function. The algorithm finds a solution, but the gradient at the solution is not close to zero. What can be done in that case?

sol3 = optimize(θ -> -obj(θ), sol1.minimizer, NewtonTrustRegion(),
        Optim.Options(extended_trace=true, store_trace=true, show_trace=true, iterations=10_000, g_tol=1e-6);
        autodiff=:finite)

julia> sol3
 * Status: success

 * Candidate solution
    Final objective value:     2.505956e+05

 * Found with
    Algorithm:     Newton's Method (Trust Region)

 * Convergence measures
    |x - x'|               = 0.00e+00 ≤ 0.0e+00
    |x - x'|/|x'|          = 0.00e+00 ≤ 0.0e+00
    |f(x) - f(x')|         = 0.00e+00 ≤ 0.0e+00
    |f(x) - f(x')|/|f(x')| = 0.00e+00 ≤ 0.0e+00
    |g(x)|                 = 1.70e+07 ≰ 1.0e-06

 * Work counters
    Seconds run:   4957  (vs limit Inf)
    Iterations:    42
    f(x) calls:    33
    ∇f(x) calls:   35
    ∇²f(x) calls:  3

julia> FiniteDiff.finite_difference_gradient(obj, sol3.minimizer) |> norm
2.1403981052614696e7