I have the following function:
$$ \max_{n_j} \sum_{j \in J_i} min( b(n_j) , Q - \sum_{k < j} b(n_k) ))$$
From my understanding minimum function is not implemented in PySCIPOpt, thus I wrote minimum as
$$ min(a , b) = \frac{(a + b - |a - b|)}{2}. $$
However, suppose $j \in (1 , 2)$ , and if $n_1=1$ then $n_0=0$ or viceversa. This means that if I pick $n_0$ then the objective value becomes:
$$min(b(n_0) , Q )$$.
Viceversa, if $n_1$ is picked the objective value becomes:
$$min(b(n_1) , Q) $$
However if I use $min(a , b) = \frac{(a + b - |a - b|)}{2}$ when $n_0=1$ I have the following result:
$$\frac{b(n_0) + Q - |b(n_0)-Q|}{2} + \frac{(Q - b(n_0)) - | Q + b(n_0)| }{2},$$ which does not guarantee that the second term is equal to 0. Do you know how can I solve this?
