erf() not defined when solving NL optimization problem with JuMP - julia

Question

I'm solving a non-linear optimization problem with JuMP in Julia, there is an erf() called in my objective function. My code throws an error saying that erf() function is not defined.
I have called Pkg.update(), loaded the SpecialFunction package and swtiched among different solvers (NLopt, Itopt) but none of them worked.
Here follows the environment and the minimized code which I tested under Julia 1.0.3
julia> versioninfo()
Julia Version 1.0.3
Commit 099e826241 (2018-12-18 01:34 UTC)
Platform Info:
OS: Windows (x86_64-w64-mingw32)
CPU: Intel(R) Core(TM) i7 CPU 860 # 2.80GHz
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-6.0.0 (ORCJIT, nehalem)
Environment:
JULIA_EDITOR = "C:\Users\binha\AppData\Local\atom\app-1.34.0\atom.exe" -a
JULIA_NUM_THREADS = 4
julia> Pkg.installed()
Dict{String,Union{Nothing, VersionNumber}} with 25 entries:
"Statistics" => nothing
"GR" => v"0.37.0"
"Distributions" => v"0.16.4"
"Random" => nothing
"Atom" => v"0.7.14"
"UUIDs" => nothing
"FastGaussQuadrature" => v"0.3.2"
"JuMP" => v"0.18.5"
"Juno" => v"0.5.4"
"LinearAlgebra" => nothing
"Ipopt" => v"0.5.1"
"NLopt" => v"0.5.1"
"PyCall" => v"1.18.5"
"LaTeXStrings" => v"1.0.3"
"SymPy" => v"0.8.3"
"StatsBase" => v"0.27.0"
"Plots" => v"0.22.5"
"PyPlot" => v"2.7.0"
"ProgressMeter" => v"0.9.0"
"QuadGK" => v"2.0.3"
"NLsolve" => v"3.0.1"
"SpecialFunctions" => v"0.7.2"
"ECOS" => v"0.9.4"
"PoissonRandom" => v"0.4.0"
"PlotlyJS" => v"0.12.2"
julia> using JuMP
julia> using NLopt
julia> using SpecialFunctions
julia> erf(1)
0.8427007929497149
julia> m=Model(solver=NLoptSolver(algorithm=:LD_MMA))
Feasibility problem with:
* 0 linear constraints
* 0 variables
Solver is NLopt
julia> #variable(m,x,start=0.0)
x
julia> #NLobjective(m,Min,erf(x))
JuMP.NonlinearExprData(ReverseDiffSparse.NodeData[NodeData(CALLUNIVAR, 53, -1), NodeData(VARIABLE, 1, 1)], Float64[])
julia> solve(m)
ERROR: UndefVarError: erf not defined
Stacktrace:
[1] #forward_eval#7(::ReverseDiffSparse.UserOperatorRegistry, ::Function, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{ReverseDiffSparse.NodeData,1}, ::SparseArrays.SparseMatrixCSC{Bool,Int64}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}) at C:\Users\binha\.julia\packages\ReverseDiffSparse\gvK2V\src\forward.jl:380
[2] #forward_eval at .\none:0 [inlined]
[3] forward_eval_all(::JuMP.NLPEvaluator, ::Array{Float64,1}) at C:\Users\binha\.julia\packages\JuMP\PbnIJ\src\nlp.jl:445
[4] eval_grad_f(::JuMP.NLPEvaluator, ::Array{Float64,1}, ::Array{Float64,1}) at C:\Users\binha\.julia\packages\JuMP\PbnIJ\src\nlp.jl:496
[5] initialize(::JuMP.NLPEvaluator, ::Array{Symbol,1}) at C:\Users\binha\.julia\packages\JuMP\PbnIJ\src\nlp.jl:403
[6] loadproblem!(::NLopt.NLoptMathProgModel, ::Int64, ::Int64, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Array{Float64,1}, ::Symbol, ::JuMP.NLPEvaluator) at C:\Users\binha\.julia\packages\NLopt\eqN9a\src\NLoptSolverInterface.jl:117
[7] _buildInternalModel_nlp(::Model, ::JuMP.ProblemTraits) at C:\Users\binha\.julia\packages\JuMP\PbnIJ\src\nlp.jl:1244
[8] #build#123(::Bool, ::Bool, ::JuMP.ProblemTraits, ::Function, ::Model) at C:\Users\binha\.julia\packages\JuMP\PbnIJ\src\solvers.jl:304
[9] #build at .\none:0 [inlined]
[10] #solve#120(::Bool, ::Bool, ::Bool, ::Base.Iterators.Pairs{Union{},Union{},Tuple{},NamedTuple{(),Tuple{}}}, ::Function, ::Model) at C:\Users\binha\.julia\packages\JuMP\PbnIJ\src\solvers.jl:168
[11] solve(::Model) at C:\Users\binha\.julia\packages\JuMP\PbnIJ\src\solvers.jl:150
[12] top-level scope at none:0
Is there any way to call erf() here with the solver?

Answer 1

Registering a custom function should help here:
julia> using JuMP, NLopt, SpecialFunctions
julia> f(x) = erf(x)
f (generic function with 1 method)
julia> m=Model(solver=NLoptSolver(algorithm=:LD_MMA))
Feasibility problem with:
* 0 linear constraints
* 0 variables
Solver is NLopt
julia> JuMP.register(m, :f, 1, f, autodiff=true)
julia> #variable(m,x,start=0.0)
x
julia> #NLobjective(m,Min,f(x))
JuMP.NonlinearExprData(ReverseDiffSparse.NodeData[NodeData(CALLUNIVAR, 73, -1), NodeData(VARIABLE, 1, 1)], Float64[])
julia> solve(m)
:Optimal
julia> getvalue(x)
-4.107514124511155