Unimodal function

A real function on an interval is unimodal if there is a point $m$ such that it is nondecreasing to the left of $m$ and nonincreasing to the right. This convention describes a single peak and allows flat regions. Some optimization texts instead use the corresponding single-valley convention, so the direction must be specified.

For example, $f(x)=-(x-2{)}^2$ has its peak at $2$. A unimodal density can describe a distribution with one mode, while unimodality of an objective allows interval-elimination search methods. Concavity implies peak unimodality, but unimodality alone does not require the chord inequalities of concavity.