凸组合是指，假设x₁,x₂,...,x_n是一组对象（要根据讨论问题的背景来确定），a₁,a₂,...,a_n是n个常数，并且满足a₁+a₂+...+a_n=1，那幺a₁x₁+a₂x₂+...+a_nx_n，并且要求每个a_i都大于等于零，就称为x₁,x₂,...,x_n的凸组合。

In convex geometry, a convex combination is a linear combination of points (which can be vectors, scalars, or more generally points in an affine space) where all coefficients are non-negative and sum to 1.

More formally, given a finite number of points in a real vector space, a convex combination of these points is a point of the form