Hi! I am trying to minimize a likelihood function for a large number of parameters. Since, the problem is quite large it would be very useful to pass the analytical gradients and the Hessian into the optimization problem. However, for some reason it is not working, when I pass the gradients and the Hessian into the second function the optimization takes forever as if it was not updating.

Also, if anybody has suggestions into how to make the functions faster and more efficient I would appreciate it a lot.

See the following MWE

```
using Optim, NLSolversBase, Random
using LinearAlgebra
###############################################################
# Loglikelihood
###############################################################
const J = 75 # This is greek letter \Iota
const Ι = 10
const N = 1000
const Mat1 = ones(Int8,Ι,N)
const Mat2 = ones(Int8,J,N)
const Mat3 = rand(Ι,J,N) .>0.9
NumberParams = Ι
const τ = rand(Ι,J)
#NumberParams = 2
function Log_Likelihood(N,Ι,J,τ,Mat1,Mat2,Mat3,params)
llike = 0.0
θ = params[1]
γ = params[2:end]
γ = vcat(γ,1.0)
pvals = zeros(Real,Ι,J,N)
for n = 1 : N , j = 1 : J
denom_index = 0.0 :: Real
for i = 1 : Ι
denom_index += Mat2[j,n]*Mat1[i,n]*exp(-θ*τ[i,j]+ γ[i])
end
for i = 1 : Ι
llike += Mat3[i,j,n]*Mat2[j,n]*Mat1[i,n]*(-θ*τ[i,j] + γ[i] - log(denom_index))
end
end
llike = -llike
end
function fgh!(F,G,H,params)
p = size(params)[1]
vec=zeros(p)
mat=zeros(p,p)
llike = 0.0
θ = params[1]
γ = params[2:end]
γ = vcat(γ,1.0)
pvals = zeros(Real,Ι,J,N)
for n = 1 : N , j = 1 : J
denom_index = 0.0 :: Real
for i = 1 : Ι
denom_index += Mat2[j,n]*Mat1[i,n]*exp(-θ*τ[i,j]+ γ[i])
end
for i = 1 : Ι
pvals[i,j,n] = Mat2[j,n]*Mat1[i,n]*(-θ*τ[i,j] + γ[i] - log(denom_index))
llike += Mat3[i,j,n]*pvals[i,j,n]
xvec = vcat(τ[i,j],zeros(Ι))
xvec[i+1] = 1
mat .+= (Mat2[j,n]*Mat1[i,n]*exp(pvals[i,j,n])*xvec*xvec')[1:end-1,1:end-1]
end
end
if G != nothing
Difference = Mat3-exp.(pvals)
for n = 1 : N , j = 1 : J
for i = 1 : Ι
vec[1] += Mat2[j,n]*Mat1[i,n]*Difference[i,j,n]*τ[i,j]
end
vec[2:end] += (Mat2[j,n]*(Mat1[:,n].*Difference[:,j,n])'*I)[1:end-1]
end
G .= vec
end
if H != nothing
H .= mat
end
F == nothing || return -llike
nothing
end
Gtest = zeros(NumberParams)
Htest = zeros(NumberParams,NumberParams)
fgh!(0,Gtest,Htest,ones(NumberParams))
func = TwiceDifferentiable(vars -> Log_Likelihood(N,Ι,J,τ,Mat1,Mat2,Mat3,vars[1:NumberParams]),
ones(NumberParams); autodiff=:forward);
opt1 = @time Optim.optimize(func, ones(NumberParams),show_trace = true)
parameters = Optim.minimizer(opt1)
opt_explicit = @time Optim.optimize(Optim.only_fgh!(fgh!), ones(NumberParams), Optim.Newton())
parameters_explicit = Optim.minimizer(opt_explicit)
```

Thanks so much