TOPICS
Search

Quasi-Convex Function


A real-valued function g defined on a convex subset C subset R^n is said to be quasi-convex if for all real alpha in R, the set {x in C:g(x)<alpha} is convex. This is equivalent to saying that g is quasi-convex if and only if its negative -g is quasi-concave.


See also

Convex, Convex Function, Pseudoconcave Function, Pseudoconvex Function, Quasi-Concave Function

This entry contributed by Christopher Stover

Explore with Wolfram|Alpha

References

Borwein, J. and Lewis, A. Convex Analysis and Nonlinear Optimization: Theory and Examples. New York: Springer Science+Business Media, 2006.

Cite this as:

Stover, Christopher. "Quasi-Convex Function." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Quasi-ConvexFunction.html

Subject classifications