The post delves into trapping points in high-dimensional spaces within an ellipsoid of minimal volume, essential for robust optimization. It explains ellipsoid representation using matrices and parametrization, highlighting the relationship between ellipsoids’ transformations and matrix operations. The focus is on the Minimal Volume Enclosing Ellipsoid (MVEE) problem, formulated as a convex optimization problem to find the smallest volume ellipsoid containing a set of points. The post demonstrates how the MVEE problem can be formulated as a convex Semidefinite Program, enabling efficient solutions using general-purpose algorithms. The unique connection between linear algebra concepts and practical applications like portfolio optimization is intriguing.
https://www.adrianriv.com/blog/2024/02/19/minimum_volume_ellipsoid/