Talk:Quasiconvex function

Redirects

I've just made several pages redirect here; this is the only actual article that deals with weak or strict quasiconcavity or quasiconvexity. Relatedly, I deleted the "see also" link to the nonexistent article on strict quasiconvexity, including a definition here. Tobacman 23:04, 9 October 2006 (UTC)[reply]

Optimization

Would it be accurate to say that quasiconvex optimization takes advantage of the property that "going down hill" always moves you closer to the minimum and that this is why convex and quasiconvex optimization is easier than optimizing over other functions? (I had a long discussion on Talk:Convex optimization; I think this page is the better place for it.) —Ben FrantzDale 17:31, 12 February 2007 (UTC)[reply]

Going downhill always moves you always to minimum, regardless of whether the function is convex or not. Did you mean "moves you closer to a global minimum"? Oleg Alexandrov (talk) 03:59, 13 February 2007 (UTC)[reply]

In 1D, perhaps, but in general there are non-convex functions with a single minimum for which moving down hill will move you away from the minimum even if subsequent steps down hill would eventually get you there. For example, consider a hill sorrounded by a moat where the moat is deepest on the East side. If you are on the West side of the hill, going down hill moves you West, away from the deep part of the moat. Continuing down hill you would find the shallow side of the moat, then wander your way around to the deep end. —Ben FrantzDale 05:33, 13 February 2007 (UTC)[reply]

OK, I don't know how to answer your question. Note by the way that "going downhill" thing has a name, it is called gradient descent. Oleg Alexandrov (talk) 16:01, 13 February 2007 (UTC)[reply]