Fejér* monotonicity in optimization algorithms
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.
Authors
- Ademir A. Ribeiro (ORCID: https://orcid.org/0000-0001-9176-2999)
- Yunier Bello-Cruz (ORCID: https://orcid.org/0000-0002-7877-5688)
- Roger Behling (ORCID: https://orcid.org/0000-0002-5473-4654)
- Alfredo N. Iusem (ORCID: https://orcid.org/0000-0002-5748-2501)
- Luiz-Rafael Santos (ORCID: https://orcid.org/0000-0002-0083-5871)
Institutions
- Northern Illinois University (US)
- Universidade Federal de Santa Catarina (BR)
- Fundação Getulio Vargas (BR)
- Universidade Federal do Paraná (BR)
Publication Details
- Journal
- Optimization
- Published
- 2026-05-21
- DOI
- https://doi.org/10.1080/02331934.2026.2673439
- Primary Topic
- Advanced Optimization Algorithms Research
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
- Fundação de Amparo à Pesquisa e Inovação do Estado de Santa Catarina