Nelder-Mead termination

[mzaffalon]

Nelder-Mead fails in the following two test cases: in too_many_iterations(), it reaches the correct minimum, (0,0) but it takes a few hundreds iteration before stopping: in wrong_minimum() it fails to find the minimum despite the tolerances on x and f being zero.

function obj_func(x, grad)
    r = sum(abs2, x)
    println(x, " -> ", r)
    r
end

function too_many_iterations()
    N = 2
    opt = Opt(:LN_NELDERMEAD, N)
    lower_bounds!(opt, -0.3 * ones(Float64, N))
    initial_step!(opt, 0.2 * ones(N))
    min_objective!(opt, obj_func)
    optimize(opt, ones(N))
end


function wrong_minimum()
    N = 2
    opt = Opt(:LN_NELDERMEAD, N)
    #println(stopval(opt), " ", ftol_rel(opt), " ", ftol_abs(opt), " ", xtol_abs(opt))
    lower_bounds!(opt, -0.3 * ones(Float64, N))
    initial_step!(opt, 0.7 * ones(N))
    min_objective!(opt, obj_func)
    optimize(opt, ones(N))
end

[odow]

These are both correct given the tolerances. For example:

julia> function too_many_iterations()
           N = 2
           opt = Opt(:LN_NELDERMEAD, N)
           opt.ftol_abs = 1e-2
           lower_bounds!(opt, -0.3 * ones(Float64, N))
           initial_step!(opt, 0.2 * ones(N))
           min_objective!(opt, obj_func)
           optimize(opt, ones(N))
       end
too_many_iterations (generic function with 1 method)

julia> too_many_iterations()
[1.0, 1.0] -> 2.0
[1.2, 1.0] -> 2.44
[1.0, 1.2] -> 2.44
[1.2000000000000002, 0.8] -> 2.0800000000000005
[1.0000000000000002, 0.8] -> 1.6400000000000006
[0.9000000000000004, 0.7000000000000001] -> 1.3000000000000007
[0.7000000000000002, 0.9000000000000001] -> 1.3000000000000005
[0.4500000000000002, 0.9500000000000002] -> 1.1050000000000004
[0.35000000000000053, 0.6500000000000004] -> 0.5450000000000008
[0.0250000000000008, 0.47500000000000053] -> 0.22625000000000056
[-0.3, 0.7250000000000006] -> 0.6156250000000009
[-0.3, 0.2500000000000009] -> 0.15250000000000044
[-0.3, -0.09999999999999876] -> 0.09999999999999976
[0.0250000000000008, -0.3] -> 0.09062500000000004
[0.1875000000000012, -0.3] -> 0.12515625000000044
[-0.3, -0.3] -> 0.18
[-0.21874999999999978, -0.3] -> 0.1378515624999999
[-0.05624999999999941, -0.09999999999999876] -> 0.013164062499999686
[0.02500000000000077, 1.8596235662471372e-15] -> 0.0006250000000000386
[0.3500000000000016, -0.1999999999999994] -> 0.16250000000000087
[-0.13749999999999962, -0.12499999999999892] -> 0.034531249999999625
[-0.13749999999999965, 0.17500000000000293] -> 0.04953125000000093
[-0.09687499999999954, 0.0562500000000022] -> 0.012548828125000158
[0.06562500000000085, 0.181250000000003] -> 0.03715820312500119
[-0.08671874999999951, -0.04843749999999845] -> 0.009866333007812264
[0.035156250000000805, -0.10468749999999878] -> 0.012195434570312302
[0.0021484375000007175, -0.06445312499999854] -> 0.004158821105956846
(0.0006250000000000386, [0.02500000000000077, 1.8596235662471372e-15], :FTOL_REACHED)