Abstract: In the paper we consider the problem of optimizing a function subject to orthonormality constraints. From a geometric aspect, this means optimization on Stiefel manifold. We present some practical problems written in this form. We show that under mild differentiability condition, the considered problem can be reformulated as an equivalent canonical d.c. programming problem. An adaptation of combined cone splitting / outer approximation methods is proposed for solving the problem in the canonical d.c. form.