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From: beet on 11 Jun 2010 15:30
Hi all,

I have a discrete function g: X -> R, which is "convex" in the
sense that I piecewiselinearly interpolate the function on the grid
pionts in X, I got a
convex function on a convex set X'. Suppose the domain X is a
finite set (e.g. a bounded subset of Z^n), I use piecewise linear
interpolation to construct a continuous function f, so that f=g on X,
and f is convex on X'.

My question is how to prove if I add small amount noises to the
function g, so now g' is very close to g on X, |g-g'| < \delta for all
x in X, here \delta is very small so that the corresponding
interpolation function g' has the similar shape as g does, and its
interpolated function is
quasiconvex.

Intuitively it is true that there exists such small \delta so that g'
has "quasiconvex" property, say if g' keeps the same order of function
g
values among on X.

P.S. a function f is quasiconvex iff f(ax+(1-s)y) <= max(f(x),f(y)),
as
a standard def in many textbooks.

Thanks a lot,

Beet
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Next: Wegener's Continental Drift theory may be telling on Atom Totality social acceptance Chapt 1 &3 #155; ATOM TOTALITY