Theoretical results
Proof sketch
Theorem: Under α-weak-orthogonality of v1 ... vm the row vectors of V, there exist a local minima of 4th order momentum momZ(V),4 of a sphered-zonotope Z(V) (VtV =Idn) , over Sn are O(αk)-close to each of its spanning vectors ±v1 ... ±vm
Proof Sketch: For sphered-zonotope, we still have :
- α-weak-orthogonality bounds <vi ,vj>
- Apply those bounds to 1st and 2nd order derivatives of fvj at vi
- Use Vectorial Taylor-Lagrange Theorem to conclude.