A convex combination is a linear combination, where all the coefficients are greater than 0 and sum to 1.

The Convex combination Wikipedia article gives the following example:

Given a finite number of points \(x_1, x_2, \ldots, x_n\) in a real vector space, a convex combination of these points is a point of the form

\[ a_1 x_1 + a_2 x _2 + \ldots + a_n x_n \] is a convex combination if all real numbers \(a_i \geq 0\) and \(a_1 + a_2 + \ldots + a_n = 1\)