Riemannian optimization on the simplex of positive definite matrices

06/25/2019

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by   Bamdev Mishra, et al.

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We discuss optimization-related ingredients for the Riemannian manifold defined by the constraint X_1 + X_2 + ... + X_K = I, where the matrix X_i ≻ 0 is symmetric positive definite of size n× n for all i = {1,...,K }. For the case n =1, the constraint boils down to the popular standard simplex constraint.