I have an optimization problem with $N$ linear inequality constraints and $K$ real valued parameters (e.g. $0.2\alpha_1+0.5\alpha_2\geq 0$, $K=2$) and no objective function. Here $N$ is much larger than $K$ and not all constraints have to be satisfied. The question is the following:
Find the parameters $\alpha_1,...,\alpha_K$ such that out of $N$ constraints maximum number of them ($M\leq N$) are satisfied.
Is this problem NP-Hard? What is the most effective way of solving such problems for large $N$ and $K$?