Help optimizing a non-linear objective with JuMP

Here is a very stripped down toy example that is roughly equivalent to my real problem (without any constraints):

	using JuMP
	using Ipopt

	N = 54
	r = rand(N)
	R = rand()
	model = Model(Ipopt.Optimizer)
	@variable(model, s[1:N])
		sum(abs((r[i]/s[i]) - R) for i in 1:N)

R is a “target ratio” and I would like to minimize the sum of the absolute differences between each of 54 different ratios and the target ratio by modifying the denominators s. In my actual problem, r is a 54 x 4 matrix, there are 4 target ratios, and I have constraints that each value of s can take, as well as a constraint on the sum of s (and I’m trying to minimize the sum of the sums of the absolute differences). However, with the real problem and with this stripped down version, I get the following error:


Also, if I call objective_function(model) it returns 0…Any ideas as to how I can formulate this problem?

Looks like a division by zero. Try setting a positive starting point for s.

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You should also try to add better bounds on s. Perhaps: @variable(model, s[i=1:N] >= r[i])

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