Abstract: In this paper, we considered a class of matrix trace function minimization problem under orthogonal constraints which arise in multivariate statistical analysis. Serval special forms of the considered problem model are widely used in the least square fitting of DEDICOM model and orthogonal INDSCAL model in multidimensional scaling analysis. Combining with orthogonal splitting techniques, several classical unfeasible iterative algorithms for solving manifold optimization problems are constructed to solve the underlying problem, and the iterative framework of these algorithms and the specific solution scheme of the generated subproblems are given. Some numerical tests are given to show the efficiency of the proposed methods.

Key words: orthogonal splitting, matrix trace function, orthogonal constraint, augmented Lagrangian method