Definition (one dimensional): A function \(f: \real \to \real\) is unimodal if there exists a point \(m\) such that \(f\) is monotonically increasing for \(x \le m\) and monotonically decreasing for \(x \ge m\).

Definition (multiple dimensions): A function \(f: \real^d \to \real\) is unimodal if there exists a point \(\m\) such that for all \(\norm{\u}=1\), \(f(\m + x\u)\) is a monotone decreasing function of \(x\).