Nonmonotone algorithm for minimization on closed sets with applications to minimization on Stiefel manifolds

Authors:
Juliano B. Francisco;Fermín S. Viloche Bazán
Affiliations:
Department of Mathematics, Federal University of Santa Catarina, Florianópolis, Santa Catarina, 88040-900, Brazil and ícole Nationale des Ponts et Chausseés, CERMICS. 6 et 8 avenue ...;Department of Mathematics, Federal University of Santa Catarina, Florianópolis, Santa Catarina, 88040-900, Brazil
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

A nonmonotone Levenberg-Marquardt-based algorithm is proposed for minimization problems on closed domains. By preserving the feasible set's geometry throughout the process, the method generates a feasible sequence converging to a stationary point independently of the initial guess. As an application, a specific algorithm is derived for minimization on Stiefel manifolds and numerical results involving a weighted orthogonal Procrustes problem are reported.