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Kaba
Posts:
289
Registered:
5/23/11


Re: Generalized CauchySchwarz
Posted:
Apr 11, 2012 5:57 PM


Kaba wrote: > Kaba wrote: > > Therefore, sharpening the problem, the problem is to characterize when > > triangle inequality holds if B is indefinite. > > Let's not forget: > > Triangle inequality holds for f > <=> > The sublevel sets of f are convex (f is quasiconvex). > <=> > The f is convex. > > Here quasiconvexity happens to be equivalent to convexity although I am > not sure why (possibly because of homogenuity of f).
Scrap that. Quasiconvexity does not imply triangle inequality or convexity here. The following hold:
Triangle inequality holds for f <=> The f is convex
and
The f is convex ==> The sublevel sets of f are convex (f is quasiconvex).
 http://kaba.hilvi.org



