Convex set

A set $$C$$ is convex. if the line segment between two points in $$C$$ lies in $$C$$, i.e., if $$\theta x_1 + (1-\theta) x_2 \in C$$ and $$0 \le \theta \le 1$$.

Convex Combination
A linear combination of points $$\sum_{i} \theta_i x_i$$ where $$\sum_i \theta_i = 1$$ and $$\theta_i \ge 0$$ is a convex combination