Tywin Lannister seems like a smart guy who wouldn't miss something as apparent as Joffrey not being Robert's son. At the same time, he has shown he cares about his family's honor and reputation (for example, by his hostile attitude towards Tyrion's hookers).

At the point of the story where *Clash of Kings* ends, is he aware of Joffrey's true parentage? If so, has he shown any concern about this?

You're welcome to include references to the later books if those make it clearer what Tywin knew at this stage, but please enclose substantial events in spoiler markup.