I think the choice is either a discussion like this - back and forth on our talk pages, or a discussion on the talk pages of the article in questiont.

It seems clear that the function ${\displaystyle F(x,y,\lambda )}$ cannot have a local extremum (at least not a strict one) as at the critical points one has ${\displaystyle g(x,y)=c}$ so that ${\displaystyle F(x*,\,y*,\,\lambda )=F(x*,\,y*,\,\lambda *)}$ for all ${\displaystyle \lambda }$. Though that doesn't quite show it to be a saddle.

By the way, if you want to add a reference to your own paper, it is best to put it on the talk page, and let someone else judge whether it should be added. If you add it yourself, you leave yourself open to accusations of using wikipedia for personal ends! Simplifix (talk) 20:29, 28 December 2008 (UTC)Reply

I think you're right. It was f I meant, not F. It is after all the properties of f that one is interested in. I think you should just undo my change, if you're sure you're right. Simplifix (talk) 18:01, 18 December 2008 (UTC)Reply