On Minimization of Sums of Heterogeneous Quadratic Functions on Stiefel Manifolds

摘要: The minimization of functions Σ i=1 k 1/2x i T A x is studied under the constraint that vectors 1, 2, ..., ∈ R n form an orthonormal system and , (k ≤ n) are given symmetric × matrices. set feasible points determines a differentiable manifold introduced by Stiefel in 1935. optimality conditions obtained global Lagrange multiplier rule, variable metric methods along geodesics suggested as solving for which convergence theorem proved. Such problems arise various situations multivariate statistical analysis.