# Question about complexity of TSP Optimization problem

Is this statement true?

Optimization TSP problems are known to be NP-hard, as we do not have a minimum cost to compare against, and in order to verify a solution is optimal, we need to iterate across the solution space.

Further, because NP-hardness is precisely defined, a problem is not NP-hard because "we do not have a minimum cost to compare against", but because for every problem $$X$$ in NP there is a polynomial-time reduction to the problem in question - by definition.