Fejér* monotonicity in optimization algorithms
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911627287199744 |
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| author | Behling, Roger Bello-Cruz, Yunier Iusem, Alfredo Noel Ribeiro, Ademir Alves Santos, Luiz-Rafael |
| author_facet | Behling, Roger Bello-Cruz, Yunier Iusem, Alfredo Noel Ribeiro, Ademir Alves Santos, Luiz-Rafael |
| contents | Fejér monotonicity is a well-established property often observed in sequences generated by optimization algorithms. In this paper, we study an extension of this property, called Fejér* monotonicity, which was initially proposed in [SIAM J. Optim., 34(3), 2535-2556 (2024)]. We discuss and explore its behavior within Hilbert spaces as a tool for optimization algorithms. Additionally, we investigate weak and strong convergence properties of this novel concept. Through illustrative examples and insightful results, we contrast Fejér* with weaker notions of quasi-Fejér-type monotonicity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_08331 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fejér* monotonicity in optimization algorithms Behling, Roger Bello-Cruz, Yunier Iusem, Alfredo Noel Ribeiro, Ademir Alves Santos, Luiz-Rafael Optimization and Control 49M27, 65K05, 65B99, 90C25 Fejér monotonicity is a well-established property often observed in sequences generated by optimization algorithms. In this paper, we study an extension of this property, called Fejér* monotonicity, which was initially proposed in [SIAM J. Optim., 34(3), 2535-2556 (2024)]. We discuss and explore its behavior within Hilbert spaces as a tool for optimization algorithms. Additionally, we investigate weak and strong convergence properties of this novel concept. Through illustrative examples and insightful results, we contrast Fejér* with weaker notions of quasi-Fejér-type monotonicity. |
| title | Fejér* monotonicity in optimization algorithms |
| topic | Optimization and Control 49M27, 65K05, 65B99, 90C25 |
| url | https://arxiv.org/abs/2410.08331 |