How to solve conditional least square?

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I'm studying least square, so I can calculate optimal solution at overdetermined system. weighted least square

But when some conditions are given, I can't calculate optimal solution(sub?) For example,

  • $ax+by>c$,
  • $a_1x+b_1y>c_1$,
  • $a_2x+b_2y>c_2$
  • ...

10 functions x and y are bigger than a10x+b10y=c10 Example How to solve this? (I want find a optimal point that makes all anX+bnY are bigger than cn)

Thank you!!