The generalized trace ratio problem {\rm (GTRP)} is to maximize a quadratic fractional objective function in trace formulation over the Stiefel manifold. In this paper, based on a newly developed matrix S-lemma, we show that {\rm (GTRP)}, if a redundant constraint is added and well scaled, has zero Lagrangian duality gap. However, this is not always true without the technique of scaling or adding the redundant constraint.
@article{arxiv.2411.09187,
title = {Closing the duality gap of the generalized trace ratio problem},
author = {Meijia Yang and Yong Xia},
journal= {arXiv preprint arXiv:2411.09187},
year = {2024}
}