Advanced · Research
Convex set
Visual diagram · (in preparation) · Math · (in preparation) · Worked example · 3 difficulty levels.
TL;DR. A geometric set where the line segment connecting any two points within the set is entirely contained within that set.
Technical Definition
A geometric set where the line segment connecting any two points within the set is entirely contained within that set.
How it works
A convex set is a region in space where, for any two points selected within the set, the straight line connecting those two points lies entirely within the same set. Think of shapes like circles, squares, or triangles – any line drawn between two points inside them stays inside. Sets containing 'dents' or 'holes', like a crescent moon or a star, are not convex sets because a line segment might pass outside the set.
Related Concepts
- Optimization — The mathematical process of finding parameter values that minimize a loss function.
- Convex function — A mathematical function shaped like a 'U', where the line segment connecting any two points on the graph lies above or on the graph itself.