Fails to converge with autodiff = :forward

[EdsterG]

The following snippet seems to never converge, might even be an infinite loop.

    import Optim

    c = 0.46827885610377784
    g = [-0.017808551990403484, -0.009150354124211798, 0.023989940649623325, -0.0015879460060053466, -0.0030085905935535303]
    H = [-1.4083929846267207 -0.08729658128691528 1.1062858720713942 0.010727524904536382 0.006676603598248883;
         -0.08729658128691528 -0.02571314825119676 0.026159077016407118 -0.0012507499641383534 -0.015024125029329585;
          1.1062858720713942 0.026159077016407118 -1.2014469206354028 -0.00606355787389272 -0.0071288964953479085;
          0.010727524904536382 -0.0012507499641383534 -0.00606355787389272 -0.0025608299686474597 0.0058944641908055245;
          0.006676603598248883 -0.015024125029329585 -0.0071288964953479085 0.0058944641908055245 0.015761181422473437]
    lb = [-0.19119409272715046, -0.78118946939934, -0.22241627896062094, -0.16624708126377563, -4.449294665337389e-17]
    ub = [0.19119409272715046, 0.78118946939934, 0.22241627896062094, 0.8336529187362244, 0.611545827757757]

    result = Optim.optimize(
        x -> -1e4 * (c + g'*x + 0.5 * x'*H*x),
        lb, ub, zeros(length(g)),
        Optim.Fminbox(Optim.BFGS()),
        Optim.Options(; show_trace=true);
        autodiff = :forward,
    )

and if you re-run the same snippet without autodiff = :forward it converges immediately.

[pkofod]

We would have to analyze the finer details here, but I agree, it does not go as expected. However, changing the starting values does help in this case

julia> result = Optim.optimize(
              x -> -1e4 * (c + g'*x + 0.5 * x'*H*x),
              lb, ub, 0.1.+zeros(length(g)),
              Optim.Fminbox(Optim.BFGS()),
              Optim.Options(; show_trace=false, iterations=100);
              autodiff = :finite, 
          )
 * Status: success

 * Candidate solution
    Final objective value:     -4.818047e+03

 * Found with
    Algorithm:     Fminbox with BFGS

 * Convergence measures
    |x - x'|               = 1.57e-16 ≰ 0.0e+00
    |x - x'|/|x'|          = 1.20e-16 ≰ 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)|                 = 4.51e-06 ≰ 1.0e-08

 * Work counters
    Seconds run:   0  (vs limit Inf)
    Iterations:    6
    f(x) calls:    559
    ∇f(x) calls:   559


julia> result = Optim.optimize(
              x -> -1e4 * (c + g'*x + 0.5 * x'*H*x),
              lb, ub, 0.1.+zeros(length(g)),
              Optim.Fminbox(Optim.BFGS()),
              Optim.Options(; show_trace=false, iterations=100);
              autodiff = :forward, 
          )
 * Status: success

 * Candidate solution
    Final objective value:     -4.818047e+03

 * Found with
    Algorithm:     Fminbox with BFGS

 * Convergence measures
    |x - x'|               = 1.57e-16 ≰ 0.0e+00
    |x - x'|/|x'|          = 1.20e-16 ≰ 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)|                 = 2.76e-06 ≰ 1.0e-08

 * Work counters
    Seconds run:   1  (vs limit Inf)
    Iterations:    6
    f(x) calls:    7568
    ∇f(x) calls:   7568