**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Carathéodory's theorem (convex hull)

Summary

Carathéodory's theorem is a theorem in convex geometry. It states that if a point x lies in the convex hull \mathrm{Conv}(P) of a set P\subset \R^d, then x can be written as the convex combination of at most d+1 points in P. More sharply, x can be written as the convex combination of at most d+1 extremal points in P, as non-extremal points can be removed from P without changing the membership of x in the convex hull.
Its equivalent theorem for conical combinations states that if a point x lies in the conical hull \mathrm{Cone}(P) of a set P\subset \R^d, then x can be written as the conical combination of at most d points in P.
The similar theorems of Helly and Radon are closely related to Carathéodory's theorem: the latter theorem can be used to prove the former the

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related concepts

Related publications

No results

No results

Related people

No results

Related units

No results

Related courses

No results

Related lectures

No results