Cone (convex cone)

A convex cone is a collection of vectors in space with two main properties: if you add any two vectors within the cone, the result stays inside the cone; and if you multiply any vector in the cone by a positive number, it remains inside the cone. Think of it as a shape that extends infinitely outward from a point, always "opening" in certain directions, with no gaps or indentations. In mathematics and optimization, convex cones help define feasible regions and constraints, providing a structured way to analyze problems involving direction and scale.