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Fejer* monotonicity in optimization algorithms
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DOI：10.1080/02331934.2026.2673439.png)
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Abstract
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Fejer 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 Fejer* 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 Fejer* with weaker notions of quasi-Fejer-type monotonicity.
Keywords:
Fejer* monotonicity
Fejer monotonicity
convex analysis
optimization algorithms
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124
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