CODEWITHSUNDEEP
optimizationjulia
Chang
Chang

Reputation: 83

Domain error when using Nelder Mead algorithm in Julia

I am struggling with optimization in Julia.

I used to use Matlab but I am trying to work on Julia instead.

The following is the code I wrote.

using Optim

V = fill(1.0, (18,14,5))
agrid  = range(-2, stop=20, length=18)
dgrid  = range(0.01, stop=24, length=14)
#zgrid  = [0.5; 0.75; 1.0; 1.25; 1.5]
zgrid  = [0.7739832502827438; 0.8797631785217791; 1.0; 1.1366695315439874; 1.2920176239404275]
# function
function adj_utility(V,s_a,s_d,s_z,i_z,c_a,c_d)
    consumption = s_z + 1.0125*s_a + (1-0.018)*s_d - c_a - c_d - 0.05*(1-0.018)*s_d
    if consumption >= 0
        return (1/(1-2)) * ((   (consumption^0.88) * (c_d^(1-0.88))   )^(1-2))
    end
    if consumption < 0
        return -99999999
    end
end

# Optimization

    i_a = 1
    i_d = 3
    i_z = 1
    utility_adj(x) = -adj_utility(V,agrid[i_a],dgrid[i_d],zgrid[i_z],i_z,x[1],x[2])
    result1 = optimize(utility_adj, [1.0, 1.0], NelderMead())

If I use zgrid = [0.5; 0.75; 1.0; 1.25; 1.5], then the code works.

However, if I use zgrid = [0.7739832502827438; 0.8797631785217791; 1.0; 1.1366695315439874; 1.2920176239404275], I got an error message "DomainError with -0.3781249999999996"

In the function, if the consumption is less than 0 then the value should be -9999999 so I am not sure why I am getting this message.

Any help would be appreciated.

Thank you.

Upvotes: 1

Views: 353

Answers (1)

Jack Shannon
Jack Shannon

Reputation: 216

Raising negative numbers to non-integer powers returns complex numbers, which is where your error is coming from.

julia> (-0.37)^(1-0.88)
ERROR: DomainError with -0.37:
Exponentiation yielding a complex result requires a complex argument.
Replace x^y with (x+0im)^y, Complex(x)^y, or similar.
Stacktrace:
 [1] throw_exp_domainerror(::Float64) at ./math.jl:37
 [2] ^(::Float64, ::Float64) at ./math.jl:888
 [3] top-level scope at REPL[5]:1

You have a constraint that consumption must be strictly positive, but if you want consumption to be a real number you will need constraints that c_d is positive as well. You can either add this directly to your objective function as above, or you can use one of the constrained optimization algorithms in NLopt, which is available in Julia via the NLopt package.

Upvotes: 1

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