Fej\'er* monotonicity in optimization algorithms
Optimization and Control
2026-04-29 v3
Abstract
Fej\'er 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 Fej\'er* 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 Fej\'er* with weaker notions of quasi-Fej\'er-type monotonicity.
Keywords
Cite
@article{arxiv.2410.08331,
title = {Fej\'er* monotonicity in optimization algorithms},
author = {Roger Behling and Yunier Bello-Cruz and Alfredo Noel Iusem and Ademir Alves Ribeiro and Luiz-Rafael Santos},
journal= {arXiv preprint arXiv:2410.08331},
year = {2026}
}