As in the case of decision problem we will introduce the notion of reducibility between two optimisation problems basically an approximation preserving reducibility which allows us to say that a problem A is easier to approximate than a problem B, in the sense that is we have an approximation algorithm for problem B that we can develop an approximation algorithm for problem A.
The notion of reducibility that we will introduce is the AP reducibility as a special case of AP reducibility and we will also define the reduction technique which as far as I know is the most used technique to prove reducibility among optimization problems.
I will give you several examples. For instance, I will be able to show that maximum clique and maximum independent set are not in the class APX, or that maximum 2-sat, maximum nae 3 sat, maximum sat(b), all these problems do not admit a polynomial time approximation scheme.
