Optimization error when using JuMP

Specific Domains Optimization (Mathematical)
2

First: Lnom, xLdf, yLdf are not defined in your example, but I am assuming you have them somewhere.
Second: your α doesn’t give any value if x is smaller than Lmin or larger than Lmax. You start the optization with x=0.5 <Lmin=0.8, so it will not run. Even if you start somewhere else, like x=1, then Ipopt may run into trouble when solving the problem.

This runs:

using JuMP, Ipopt

const R0 = 0.1803

Lmin, Lmax = 0.8, 3.5
Lnom = 2.0
w1 = 0.4

w2 = 0.6

Rfc1 = 0.1803 + 0.01

Rfc2 = 0.1803

L11, L21 = 2.1, 2.1

Dindf = repeat([250], 2)

Ldf = [5, 4]



function α(x)
    a = 0.0019727939
    b = 0.0078887
    α_0 = 0.006226
    if Lmin <= x < Lnom
        return a * (x - Lnom)^2 + α_0
    elseif Lnom <= x <= Lmax
        return b * (x - Lnom)^2 + α_0
    else
        return 0.0 ##New part here
    end
end
function obj(x, y)
    f0dL = (w1 * (Ldf[1] - L11)^2 + w2 * (Ldf[1] - L21)^2) * 1 * 3600
    return (w1 * α(x)) * Dindf[1] + f0dL
end



model = Model(Ipopt.Optimizer)

lb = maximum(Lmin ./ Ldf)

ub = minimum(Lmax ./ Ldf)

@variable(model, lb <= x <= ub, start = 1.0)

@variable(model, lb <= y <= ub, start = 1.0)

@NLconstraint(model, x + y == 1)

register(model, :obj, 2, obj; autodiff = true)

@NLobjective(model, Min, obj(x, y))

optimize!(model)

(I created the missing values)

I think you α needs work outside Julia. How is it possible to require x>=0.8, y>=0.8 in α(x),α(y) and then enforce constraint x+y=1?

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