In computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems.
Typically such limits show a factor of approximation beyond which a problem becomes NP-hard, implying that finding a polynomial time approximation for the problem is impossible unless NP=P.
Some hardness of approximation results, however, are based on other hypotheses, a notable one among which is the unique games conjecture.
Since the early 1970s it was known that many optimization problems could not be solved in polynomial time unless P = NP, but in many of these problems the optimal solution could be efficiently approximated to a certain degree.
For an example of an NP-hard optimization problem that is hard to approximate, see set cover.