Benchmark of Nelder-Mead algorithms

anms.patch

diff --git a/src/ANMS.jl b/src/ANMS.jl
index b235efd..5f93caa 100644
--- a/src/ANMS.jl
+++ b/src/ANMS.jl
@@ -72,6 +72,7 @@ function nelder_mead(f::Function, x₀::Vector{Float64}; iterations::Int=1_000_0
     u = zeros(n)
     for i in 1:n
         τ = x₀[i] == 0.0 ? 0.00025 : 0.05
+        τ = 1.0
         u[i] = 1.0
         x = x₀ .+ τ * u
         u[i] = 0.0
@@ -214,6 +215,8 @@ function nelder_mead(f::Function, x₀::Vector{Float64}; iterations::Int=1_000_0
                 break
             end
         end
+        # same as Optim.jl
+        fvalconv = domconv = sqrt(var(fvalues) * (n / (n+1))) < ftol
 
         iter += 1
     end

bench.jl

function quadratic(x)
    x = x .- 1.0
    dot(x, x)
end

function rosenbrock(x)
    N = length(x)
    fval = 0.0
    for i in 1:div(N, 2)
        fval += 100(x[2i-1]^2 - x[2i])^2 + (x[2i-1] - 1.0)^2
    end
    fval
end

const f = rosenbrock
const ns = [2, 5, 10, 20, 50]
const I = 10

import ANMS
let
    println("--- ANMS ---")
    x₀ = zeros(2)
    ANMS.nelder_mead(f, x₀)

    for n in ns
        x₀ = zeros(n)
        println("$n: ")
        gc()
        local fmin
        @time for i in 1:I
            _, fmin = ANMS.nelder_mead(f, x₀, iterations=1_000_000)
        end
        @show fmin
    end
    println()
end

import Optim
let
    println("--- Optim ---")
    x₀ = zeros(2)
    Optim.nelder_mead(f, x₀)

    for n in ns
        x₀ = zeros(n)
        println("$n: ")
        gc()
        local fmin
        @time for i in 1:I
            r = Optim.nelder_mead(f, x₀, iterations=1_000_000)
            fmin = r.f_minimum
        end
        @show fmin
    end
    println()
end

quadratic.txt

--- ANMS ---
2: 
elapsed time: 0.010157602 seconds (157552 bytes allocated)
fmin => 0.0
5: 
elapsed time: 0.00133118 seconds (889680 bytes allocated)
fmin => 2.874692204466751e-8
10: 
elapsed time: 0.003661411 seconds (2564752 bytes allocated)
fmin => 5.704532655372583e-8
20: 
elapsed time: 0.011579524 seconds (8133728 bytes allocated)
fmin => 5.1698486524263214e-8
50: 
elapsed time: 0.068112864 seconds (42861936 bytes allocated)
fmin => 8.513696765777041e-8

--- Optim ---
2: 
elapsed time: 0.017564181 seconds (348568 bytes allocated)
fmin => 9.397767141614407e-10
5: 
elapsed time: 0.002295282 seconds (2651920 bytes allocated)
fmin => 1.3461476385934277e-9
10: 
elapsed time: 0.016708881 seconds (20459840 bytes allocated)
fmin => 1.142383173134101e-7
20: 
elapsed time: 0.115632867 seconds (108467840 bytes allocated, 38.78% gc time)
fmin => 5.944810588990531e-8
50: 
elapsed time: 2.397011401 seconds (2835856800 bytes allocated, 49.88% gc time)
fmin => 3.663031017751178e-8

rosenbrock.txt

--- ANMS ---
2: 
elapsed time: 0.009974135 seconds (146488 bytes allocated)
fmin => 7.868156252247752e-9
5: 
elapsed time: 0.000866841 seconds (427600 bytes allocated)
fmin => 2.071245431037171e-8
10: 
elapsed time: 0.003445336 seconds (1678768 bytes allocated)
fmin => 3.996436273244788e-8
20: 
elapsed time: 0.016988347 seconds (6119008 bytes allocated)
fmin => 7.81905861025263e-8
50: 
elapsed time: 0.274938347 seconds (62309152 bytes allocated, 7.80% gc time)
fmin => 8.238820707411458e-7

--- Optim ---
2: 
elapsed time: 0.017885417 seconds (615528 bytes allocated)
fmin => 8.940245976539097e-10
5: 
elapsed time: 0.008627849 seconds (9746640 bytes allocated)
fmin => 1.250866767091252e-9
10: 
elapsed time: 0.099422094 seconds (84184160 bytes allocated, 27.03% gc time)
fmin => 0.010763954938890423
20: 
elapsed time: 0.822331694 seconds (754486560 bytes allocated, 42.30% gc time)
fmin => 0.7307076508015659
50: 
elapsed time: 31.874317729 seconds (36538050560 bytes allocated, 51.20% gc time)
fmin => 1.1993608845052381