Abstract
The minimization of functions Σ k i=1 1/2x T i A i x i is studied under the constraint that vectors x 1, x 2, ..., x k ∈ R n form an orthonormal system and A 1, ..., A k , (k ≤ n) are given symmetric n × n matrices. The set of feasible points determines a differentiable manifold introduced by Stiefel in 1935. The optimality conditions are obtained by the global Lagrange multiplier rule, and variable metric methods along geodesics are suggested as solving methods for which a global convergence theorem is proved. Such problems arise in various situations in multivariate statistical analysis.
This research was supported in part by the Hungarian National Research Foundation, Grant Nos. OTKA-T016413 and OTKA-T017241
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© 2001 Springer Science+Business Media Dordrecht
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Rapcsák, T. (2001). On Minimization of Sums of Heterogeneous Quadratic Functions on Stiefel Manifolds. In: Migdalas, A., Pardalos, P.M., Värbrand, P. (eds) From Local to Global Optimization. Nonconvex Optimization and Its Applications, vol 53. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5284-7_12
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DOI: https://doi.org/10.1007/978-1-4757-5284-7_12
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