Abstract
We study and analyze a nonmonotone globally convergent method for minimization on closed sets. This method is based on the ideas from trust-region and Levenberg-Marquardt methods. Thus, the subproblems consists in minimizing a quadratic model of the objective function subject to the constraint set. We incorporate concepts of bidiagonalization and calculation of the SVD "with inaccuracy'' to improve the performance of the algorithm, since the solution of the subproblem by traditional techniques, which is required in each iteration, is computationally expensive. Other feasible methods are mentioned, including a curvilinear search algorithm and a minimization along geodesics algorithm. Finally, we illustrate the numerical performance of the methods when applied to the Orthogonal Procrustes Problem.<object id="c828aa19-8948-aba9-58e8-19af48b78cb9" width="0" height="0" type="application/gas-events-bb"></object>
Highlights
In this paper, we consider the Weighted Orthogonal Procrustes Problem (WOPP)
The Procrustes Problem belongs to the class of minimization problems restricted to the set of matrices with orthonormal columns, which often appear in important classes of optimization
The aim of this study is to numerically compare the performance of these methods and improve the performance of the algorithm proposed in [13]
Summary
We consider the Weighted Orthogonal Procrustes Problem (WOPP). Given X ∈ Rm×n, A ∈ R p×m, B ∈ R p×q and C ∈ Rn×q , we address the following constrained optimization problem: min ||AX C − B||2F (1) s.t. X T X = I. We consider the problem when the objective function of is replaced by || A X. B||2F , called here as Orthogonal Procrustes Problem (OPP). The Procrustes Problem belongs to the class of minimization problems restricted to the set of matrices with orthonormal columns, which often appear in important classes of optimization
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