linguistic:voice_change
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.

Another definition is to require that there be a polynomial-time reduction from an NP-complete problem G to H. As any problem L in NP reduces in polynomial time to G, L reduces in turn to H in polynomial time so this new definition implies the previous one. It does not restrict the class NP-hard to decision problems, and it also includes search problems or optimization problems.