I have the problem A:
$$\min (-x_{k\{ n \}}+u*(\sum_{k=1}^{K}x_{k\{ n \}})+\sum_{k=1}^{K}y_{k\{ n \}}))$$ $$\text{where} \quad 0<x_{k\{ n \}}<l, 0<y_{k\{ n \}}<m$$
The problem is that it is better to solve the following problem B:
$$\min (u*(\sum_{k=1}^{K}x_{k\{ n \}})+\sum_{k=1}^{K}y_{k\{ n \}}))$$ where the difference is that there is not exist this term: $-x_{k\{ n \}}$.
With a good choice of constant $u$, the problems $A$ and $B$ are the same minimization problem. $u$ depends to the limits of $x_k$ and $y_k$.
How to find a good inequality of $u$ ?