Editing Unimodality (section)

==Other extensions==

A function ''f''(''x'') is "S-unimodal" (often referred to as "S-unimodal map") if its [[Schwarzian derivative]] is negative for all <math>x \ne c</math>, where <math>c</math> is the critical point.<ref>See e.g. {{cite journal|title=Distortion of S-Unimodal Maps|author1=John Guckenheimer |author2=Stewart Johnson |journal=Annals of Mathematics |series=Second Series|volume=132|number=1|date=July 1990|pages=71–130|doi=10.2307/1971501|jstor=1971501 }}</ref>

In [[computational geometry]] if a function is unimodal it permits the design of efficient algorithms for finding the extrema of the function.<ref>{{cite journal|author=Godfried T. Toussaint|title=Complexity, convexity, and unimodality|journal=International Journal of Computer and Information Sciences|volume=13|number=3|date=June 1984|pages=197–217|doi=10.1007/bf00979872|s2cid=11577312 }}</ref>

A more general definition, applicable to a function ''f''(''X'') of a vector variable ''X'' is that ''f'' is unimodal if there is a [[one-to-one function|one-to-one]] [[differentiable]] mapping ''X'' = ''G''(''Z'') such that ''f''(''G''(''Z'')) is convex.  Usually one would want ''G''(''Z'') to be [[continuously differentiable]] with nonsingular Jacobian matrix.

[[Quasiconvex function]]s and quasiconcave functions extend the concept of unimodality to functions whose arguments belong to higher-dimensional [[Euclidean space]]s.