Closing the duality gap of the generalized trace ratio problem

Meijia Yang; Yong Xia

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arXiv · 2411.09187

Closing the duality gap of the generalized trace ratio problem

Meijia Yang·Yong Xia

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Abstract

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.

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Meijia Yang, Yong Xia. 2024-11-14. Closing the duality gap of the generalized trace ratio problem. https://arxiv.org/abs/2411.09187

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