Abstract:Helly's theorem is an important result from Convex Geometry. It gives sufficient conditions for a family of convex sets to have a nonempty intersection. A large variety of proofs as well as applications are known. Helly's theorem also has close connections to two other well-known theorems from Convex Geometry: Radon's theorem and Carathéodory's theorem. In this project we study Helly's theorem and its relations to Radon's theorem and Carathéodory's theorem by using tools of Convex Analysis and Optimization. Mo… Show more
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