In this paper, we establish a continuous selection theorem and use it to derive five equivalent results on the existence of fixed points, sectional points, maximal elements, intersection points and solutions of variational relations, all in topological settings without linear structures. Then,...

Based on a novel reformulation of the feasible region, we propose and analyze a partial Lagrangian relaxation approach for the unbalanced orthogonal Procrustes problem (UOP). With a properly selected Lagrangian multiplier, the Lagrangian relaxation (LR) is equivalent to the recent matrix lifting...