MethodError: no method matching in JuMP

Specific Domains Optimization (Mathematical)
1

I am new in julia. When i use JuMP, i meet some problems: MethodError: no method matching (::Interpolations.Extrapolation{Float64, 1, ScaledInterpolation{Float64, 1, Interpolations.BSplineInterpolation{Float64, 1, Vector{Float64}, BSpline{Linear{Throw{OnGrid}}}, Tuple{Base.OneTo{Int64}}}, BSpline{Linear{Throw{OnGrid}}}, Tuple{StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}}}, BSpline{Linear{Throw{OnGrid}}}, Throw{Nothing}})(::AffExpr)
Use square brackets for indexing an Array.
Closest candidates are:
(::Interpolations.Extrapolation{T, N, ITPT, IT, ET} where {ITPT, IT, ET})(::Number…) where {T, N} at

using JuMP
import Ipopt
β = 0.88
Nb = 1000
δ = 1.5
wage = 1
rate = 1
grid_b = range(0, 5, length = 1000)
w = 5 * (grid_b).^2
w_func = LinearInterpolation(grid_b, w)
choice1 = Model(Ipopt.Optimizer)  
@variable(choice1, x >= 0)
@NLobjective(choice1, Max, x^δ/(1-δ) + β * (w_func.((grid_b[3]*(1+rate)+wage-x) * 3))) 
optimize!(choice1)
2

You can’t use arbitrary functions in JuMP. You need to use a user-defined function:
https://jump.dev/JuMP.jl/stable/manual/nlp/#User-defined-Functions

But this will only work if it’s possible to automatically differentiate the function. I don’t know if that works with Interpolations.jl.