Work

Fejér* monotonicity in optimization algorithms

Year: 2026

Type: article

Abstract: 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 behaviour 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.

Source: Optimization

DOI: 10.1080/02331934.2026.2673439

Authors: Roger Behling, Yunier Bello-Cruz, Alfredo Noel Iusem, Ademir Alves Ribeiro, Luiz-Rafael Santos

Institutions: Universidade Federal de Santa Catarina, Northern Illinois University, Fundação Getulio Vargas, Universidade Federal do Paraná

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

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

Awards: G1623638773, G1823276196, Design and Analysis of Algorithms for Structured Optimization, G5132692639