Maximize sum of the piecewise function

I am the new in JuMP package, and I am trying to solve the optimization with a piecewise function

My maximum working example looks as follows:

using JuMP, Ipopt

function sum_rate(β::T ...) where {T <: Real}
    rate = zeros(T, length(β))
    for i = 1:length(β)-1
        rate[i] = 0.5 * log2(1 + β[i]/(sum(β[i]) + 2))        
    rate[length(β)] = 0.5 * log2(1 + β[length(β)]/2)
    return sum(rate)

model = Model(Ipopt.Optimizer)
@variable(model, β[i = 1:3] >= 0)
@constraint(model, sum(β) <= 1)
@NLobjective(model, Max, sum_rate)

However, I can not pass the compile with error:

Unexpected object sum_rate of type typeof(sum_rate) in nonlinear expression.

Can anyone help me to solve this issue? Thank you!

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Hi there! Since it seems that you’re new to JuMP, you should take a read through the tutorials:

You can’t create a nonlinear objective by passing it a Julia function like that.

Do instead

@NLobjective(model, Max, sum_rate(β...)

You’ll also get a warning, so you’ll need

register(model, :sum_rate, 3, sum_rate; autodiff = true)

You should also consider writing out the expression directly. It lets JuMP compute more efficient derivatives that might improve performance.

model = Model(Ipopt.Optimizer)
@variable(model, β[i = 1:3] >= 0)
@constraint(model, sum(β) <= 1)
    sum(0.5 * log2(1 + β[i]/(β[i] + 2)) for i in 1:length(β)-1) +
    0.5 * log2(1 + β[3] / 2)

Thank you very much for the help!

1 Like