According to Wikipedia:
A convex cone is a a subset of a vector space that is closed under linear combinations with positive coefficients.
I wonder if the term 'convex' has a special meaning or geometric interpretation. Therefore, my question is: why we call it 'convex'?
A set of points is convex if the line segment connecting any two points of the set lies entirely in the set. You'd think of a shape as "concave" if you could connect two points by a line segment and part of that line segment was outside the set. So "convex" means "non concave".