The issue is the term sum(abs.(x)))
This comes up fairly often, e.g.: Abs in JuMP - #3 by odow
You need to reformulate sum(abs.(x))) as sum(t) where you’ve defined
@variable(vector_model, t[1:length(x)] >= 0)
@constraint(vector_model, [i=1:length(x)], x[i] <= t[i])
@constraint(vector_model, [i=1:length(x)], -t[i] <= x[i])