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arXiv · 2410.08331

Fej\'er* monotonicity in optimization algorithms

Roger Behling·Yunier Bello-Cruz·Alfredo Noel Iusem·Ademir Alves Ribeiro·Luiz-Rafael Santos
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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.

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Roger Behling, Yunier Bello-Cruz, Alfredo Noel Iusem, Ademir Alves Ribeiro, Luiz-Rafael Santos. 2024-10-10. Fej\'er* monotonicity in optimization algorithms. https://arxiv.org/abs/2410.08331

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