Supporting Hyperplane

A supporting hyperplane is a flat surface that touches a curved or uneven shape (called a convex set) at least at one point, without cutting through or crossing the shape. Think of it like a sheet of paper resting against a rounded object; the paper touches the object in a way that it just "supports" or touches without slicing through. In mathematical terms, it helps describe the boundary of the object and is useful in optimization problems, where it can be used to find the best solutions by "supporting" the shape at its outer edges.