Extreme Point Pursuit -- Part II: Further Error Bound Analysis and Applications
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866917832067907584 |
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| author | Liu, Junbin Liu, Ya Ma, Wing-Kin Shao, Mingjie So, Anthony Man-Cho |
| author_facet | Liu, Junbin Liu, Ya Ma, Wing-Kin Shao, Mingjie So, Anthony Man-Cho |
| contents | In the first part of this study, a convex-constrained penalized formulation was studied for a class of constant modulus (CM) problems. In particular, the error bound techniques were shown to play a vital role in providing exact penalization results. In this second part of the study, we continue our error bound analysis for the cases of partial permutation matrices, size-constrained assignment matrices and non-negative semi-orthogonal matrices. We develop new error bounds and penalized formulations for these three cases, and the new formulations possess good structures for building computationally efficient algorithms. Moreover, we provide numerical results to demonstrate our framework in a variety of applications such as the densest k-subgraph problem, graph matching, size-constrained clustering, non-negative orthogonal matrix factorization and sparse fair principal component analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06513 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extreme Point Pursuit -- Part II: Further Error Bound Analysis and Applications Liu, Junbin Liu, Ya Ma, Wing-Kin Shao, Mingjie So, Anthony Man-Cho Signal Processing Optimization and Control In the first part of this study, a convex-constrained penalized formulation was studied for a class of constant modulus (CM) problems. In particular, the error bound techniques were shown to play a vital role in providing exact penalization results. In this second part of the study, we continue our error bound analysis for the cases of partial permutation matrices, size-constrained assignment matrices and non-negative semi-orthogonal matrices. We develop new error bounds and penalized formulations for these three cases, and the new formulations possess good structures for building computationally efficient algorithms. Moreover, we provide numerical results to demonstrate our framework in a variety of applications such as the densest k-subgraph problem, graph matching, size-constrained clustering, non-negative orthogonal matrix factorization and sparse fair principal component analysis. |
| title | Extreme Point Pursuit -- Part II: Further Error Bound Analysis and Applications |
| topic | Signal Processing Optimization and Control |
| url | https://arxiv.org/abs/2403.06513 |