I am dealing with a knapsack-like problem with one difference from the conventional problem: the “weights” can be positive or negative and the constraint is $\sum w_i x_i \ge 0$ instead of $\sum w_i x_i \le W$.

Can this be transformed to a knapsack problem or is it some other type of combinatorial optimization problem?

I am dealing with a knapsack-like problem with one difference from the conventional problem: the “weights” can be positive or negative and the constraint is $\sum w_i x_i \ge 0$ instead of $\sum w_i x_i \le W$. The "values" can also be positive or negative.

Can this be transformed to a knapsack problem or is it some other type of combinatorial optimization problem?