I have a quesiton about linear programming.
My objective is trying to make the utilization evenly.
Example
$U_{1}, U_{2},...,U_{k} $
$\sum_{i=1..k} U_{i} = C $
$C$ is some constant. $U_{i}$ is our assignment.
$Objective: $ I want $U_{i}$ are as even as possible.
My question is that is the Objective be the same as minimizing $\sum_{i=1...k} (U_{i})^{2}$
If it does, then why? Is there proof of this?
Reference: My original problem is Load balancing in Multi-commodity flow problem https://en.wikipedia.org/wiki/Multi-commodity_flow_problem