Definition: A function f(x) mapping from the reals to the reals is quasiconvex if it is
nonincreasing for all values of x below some x0 and nondecreasing
for all values of x above x0. x0 can be infinity or
negative infinity: that is, a function that is everywhere nonincreasing or
nondecreasing is quasiconvex.
Quasiconvex functions have the property that for any two points in the domain, say x1 and x2, the value of f(x) on all points between them satisfies:
max{f(x1), f(x2)} => f(x).
Equivalently, f() is quasiconvex iff -f() is quasiconcave.
Equivalently, f() is quasiconvex iff for any constant real k, the set of values x in the domain of f() for which k => f(x) is a convex set.
A function that is convex over some domain is also quasiconvex over that domain. (Proven in Chiang, p 390). (Econterms)
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