Smooth maximum
In mathematics, a smooth maximum of an indexed family x1, ..., xn of numbers is a smooth approximation to the maximum function max ( x 1 , … , x n ) , {\displaystyle \max(x_{1},\ldots ,x_{n}),} meaning a parametric family of functions m α ( x 1 , … , x n ) {\displaystyle m_{\alpha }(x_{1},\ldots ,x_{n})} such that for every α {\displaystyle \alpha } , the function m α {\displaystyle m_{\alpha }} is smooth, and the family converges to the maximum function m α → max {\displaystyle m_{\alpha }\to \max } as α → ∞ {\displaystyle \alpha \to \infty } . The concept of smooth minimum is similarly defined.