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

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.