Fejér and Fejér* Monotonicity: New Results and Limiting Examples
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909970634637312 |
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| author | Arakcheev, Aleksandr Bauschke, Heinz H. |
| author_facet | Arakcheev, Aleksandr Bauschke, Heinz H. |
| contents | Many algorithms in convex optimization and variational analysis can be analyzed using Fejér monotone sequences. In 2024, Behling, Bello-Cruz, Iusem, Alves Ribeiro, and Santos introduced a new, more general, notion: Fejér* monotonicity. They obtained basic results and discussed applications in optimization.
In this work, we complement Behling et al.'s work by presenting a thorough study of Fejér* monotonicity. We reveal striking similarities and differences between these notions, including descriptions of the maximal Fejér* set. Moreover, we also touch upon Opial sequences and quasi-Fejér monotonicity. Throughout this paper, we provide numerous limiting examples and counterexamples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fejér and Fejér* Monotonicity: New Results and Limiting Examples Arakcheev, Aleksandr Bauschke, Heinz H. Optimization and Control Many algorithms in convex optimization and variational analysis can be analyzed using Fejér monotone sequences. In 2024, Behling, Bello-Cruz, Iusem, Alves Ribeiro, and Santos introduced a new, more general, notion: Fejér* monotonicity. They obtained basic results and discussed applications in optimization. In this work, we complement Behling et al.'s work by presenting a thorough study of Fejér* monotonicity. We reveal striking similarities and differences between these notions, including descriptions of the maximal Fejér* set. Moreover, we also touch upon Opial sequences and quasi-Fejér monotonicity. Throughout this paper, we provide numerous limiting examples and counterexamples. |
| title | Fejér and Fejér* Monotonicity: New Results and Limiting Examples |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2512.17039 |