Kind of optimal assignment problem

Hi all!

I have to solve a kind of optimal assignment 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. Actually, for a set of values of interest, f(s_i, a_i) is convex as well.

Can anyone help me to “code” eventually in cvx such a problem?

The use of the phrase “a generic differentiable function,… for a set of values of interest is convex as well” indicates that cvx is probably not the right tool for you. See You need a very specific f which can be represented with the DCP ruleset.

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Thank you Adam. Now, i was able to obtain a convex version of f function. Is it now possible to solve by cvx the previous problem?

It is the same answer as before - you have to write f in cvx compatible form. You did not tell us anything new compared to the first post.