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?