Quasiconvex function
（重定向自Quasiconvexity）
![A quasiconvex function that is not convex.](/Images/godic/202502/05/Quasiconvex_function3251.png")
![A function that is not quasiconvex: the set of points in the domain of the function for which the function values are below the dashed red line is the union of the two red intervals, which is not a convex set.](/Images/godic/202502/05/Nonquasiconvex_function3251.png")
![The probability density function of the normal distribution is quasiconcave but not concave.](/Images/godic/202502/05/Standard_deviation_diagram.svg3251.png")
![A quasilinear function is both quasiconvex and quasiconcave.](/Images/godic/202502/05/Monotonicity_example23251.png")
In mathematics, a quasiconvex function is a real-valued function defined on an interval or on a convex subset of a real vector space such that the inverse image of any set of the form ![(-\infty,a)](/Images/godic/202502/05/f6a9f4d938cbc5cf7941fc3550cc6fde3252.png")
is a convex set. Informally, along any stretch of the curve the highest point is one of the endpoints. The negative of a quasiconvex function is said to be quasiconcave.