Let me explain my trouble by another example.
The wiki page says that
Lattice problems are an example of NP-hard problems
However, by clicking NP-hard, i find this definition
A decision problem H is NP-hard when for every problem L in NP, there is a polynomial-time many-one reduction from L to H.
What the fact? Lattice problems are not decision problems.
Edit after two answers: I think the two answers below have contradicting definitions:
1-)An optimization problem is NP-hard if it is as hard as NP-hard decision problems.
2-) An optimization problem is NP-hard if its decision version is NP-hard.
Which one is the real definition.