“…Recently considered applications include matrix completion problems [8,21,12,33], truss optimization [26], finite-element discretization of Cosserat rods [27], matrix mean computation [6,4], and independent component analysis [31,30]. Research efforts to develop and analyze optimization methods on manifolds can be traced back to the work of Luenberger [20]; they concern, among others, steepest-descent methods [20], conjugate gradients [32], Newton's method [32,3], and trust-region methods [1,5]; see also [2] for an overview.…”