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arXiv Statistics ML By Quoc Tran-Dinh, Pham Ngoc Anh, Ha Manh Tien

Provable Parameter-Free Fixed-Point Algorithms with Linear Convergence Rates

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The paper introduces two parameter‑free Halpern fixed‑point algorithms that automatically exploit hidden contractivity without needing a prior estimate of the contraction factor. Both methods achieve explicit linear convergence rates for the fixed‑point residual and distance to the unique fixed point, with one variant using a line‑search to locally estimate the contraction factor. Extensions include parameter‑free Nesterov‑type variants and a Tikhonov‑regularized approach for cocoercive equations, yielding an iteration complexity of \(\mathcal{O}(\epsilon^{-1}\log(\epsilon^{-1}))\).

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