Optimization problem (optimal assignment like)

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Mario
Mario 2020-5-4
Hi all!
I have to solve a kind of optimal assigment problem. I have 4 nodes (n_1,...,n_4) each of which can host a number of servers s_k for k=1...4 (E.g. s_3=5 means that the node 3 can host 5 servers). I would to find the minimal number of servers s_k such that:
  • s_k >= a_k at each node k, where a_k is a local "threshold" different for each node
  • f(s_1, a_1) + f(s_2, a_2) + f(s_3, a_3) + f(s_4, a_4) <= T where f(s_i, a_i) is a generic differentiable function, and T a "global" threshold.
Can anyone give help to me in finding a way of coding such a problem in matlab?

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