On minimization on Stiefel manifolds

On minimization on Stiefel manifolds

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Article ID: iaor20032075
Country: Netherlands
Volume: 143
Issue: 2
Start Page Number: 365
End Page Number: 376
Publication Date: Dec 2002
Journal: European Journal of Operational Research
Authors:
Abstract:

The minimization of a smooth function f : Rkn→R under the constraint that vectors x1, x2,...,xk∈Rn, k≤n, form an orthonormal system seems to be a new and interesting global optimization problem with important theoretical and practical applications. The set of feasible points determines a differentiable manifold introduced by Stiefel in 1935. Based on the nice geometric structure, the optimality conditions are obtained by the global Lagrange multiplier rule, and global optimality conditions based on local information, which make the advantages of using the Riemannian geometry in difficult smooth optimization problems clear.

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