Effective Algorithms for Solving Trace Minimization Problem in Multivariate Statistics

Algorithm 1

Riemannian Newton’s method for Problem 1.

(1)	Choose an initial point .
(2)	fordo
(3)	Compute that satisfies and .
(4)	Compute the partition matrix by Lemma 4 and the vector by (68). Compute that satisfies the symmetric linear equation (69).
(5)	Partition as , where .
(6)	Construct and that satisfy and .
(7)	Compute .
(8)	Compute the next iterate , where is a retraction on .
(9)	end for