{"ID":2827749,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.17039","arxiv_id":"2512.17039","title":"Fejér and Fejér* Monotonicity: New Results and Limiting Examples","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2512.17039","url_pdf":"https://arxiv.org/pdf/2512.17039v1","authors":"[\"Aleksandr Arakcheev\",\"Heinz H. Bauschke\"]","published":"2025-12-18T20:01:46Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}