Given a set $S$, a value function $v(s)$ and a cost function $c(s)$ for all $s \in S$, and integers $B$ and $K$, the classic formulation of the Knapsack problem asks if there is a subset $S' \subseteq S$ in which $\sum_{s \in S'} v(s) \geq K$ and $\sum_{s \in S'} c(s) \leq B$.
Is there a variation/special case of the Knapsack problem where there is no $B$? I read through this question: Is there a name for the knapsack problem with no bound on knapsack capacity?, but the author assumes multiple knapsacks.
One way to formulate the problem where no capacity is given could be to ask for the cheapest subset $S'$ where $\sum_{s \in S'} v(s) \geq K$, but then I'm not sure if this is still considered a Knapsack.
