Our team lead by Bamdev has presented, at NeurIPS workshop OPT2020 our work “Riemannian optimization on the simplex of positive definite matrices.”

• Riemannian optimization on the simplex of positive definite matrices
  • Author: Bamdev Mishra, HK, and Pratik Jawanpuria
  • Abstract: In this work, we generalize the probability simplex constraint to matrices, i.e., X1+X2+…+XK=I, where Xi⪰0 is a symmetric positive semidefinite matrix of size n×n for all i={1,…,K}. By assuming positive definiteness of the matrices, we show that the constraint set arising from the matrix simplex has the structure of a smooth Riemannian submanifold. We discuss a novel Riemannian geometry for the matrix simplex manifold and show the derivation of first- and second-order optimization related ingredients.

  •  publisher’s site, arXiv preprint 1906.10436