Closing the duality gap of the generalized trace ratio problem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916479962710016 |
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| author | Yang, Meijia Xia, Yong |
| author_facet | Yang, Meijia Xia, Yong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09187 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Closing the duality gap of the generalized trace ratio problem Yang, Meijia Xia, Yong Optimization and Control 90C26, 90C32, 90C46 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. |
| title | Closing the duality gap of the generalized trace ratio problem |
| topic | Optimization and Control 90C26, 90C32, 90C46 |
| url | https://arxiv.org/abs/2411.09187 |