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We study semidefinite programming (SDP) relaxations for the NP-hard problemof globally optimizing a quadratic function over the Stiefel manifold. Weintroduce a strengthened relaxation based on two recent ideas in theliterature: (i) a tailored SDP for objectives with a block-diagonal Hessian;(ii) and the use of the Kronecker matrix product to construct SDP relaxations.Using synthetic instances on four problem classes, we show that, in general,our relaxation significantly strengthens existing relaxations, although at theexpense of longer solution times.

A Strengthened SDP Relaxation for Quadratic Optimization Over the Stiefel Manifold