convex set

A convex set is a collection of points in space where, for any two points within the set, the straight line connecting them also lies entirely inside the set. Imagine a shape like a circle, a triangle, or a cube—these are convex because you can draw a straight line between any two points inside them without leaving their boundaries. Conversely, shapes with indentations, like a crescent moon, are not convex because some lines between points inside them pass outside the shape. Convex sets are fundamental in mathematics and optimization, simplifying analysis and problem-solving.