I want to solve an overdetermined system of inequalities ($ax+by \ge c$). Specifically, I have $10$ linear functions of the form $ax+by$ that must be bigger than $c$ at a point $(x,y)$. But it is good to minimize the difference between $ax+by$ and $c$. I need a formula like that (weighted overdetermined system.
I am lacking in mathematical knowledge. If you let me know the formulas and the concepts. I will solve my problem by using programming. Please help me.
overdetermined system of inequalities. violating least number of them.