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Single-call Polyak-Type Extragradient Methods for Monotone Root-Finding Problems
Abstract
We propose a single-call variant of Polyak extragradient, termed SPolyakEG, by recycling the previous extrapolation operator evaluation. Under a delayed critical condition, we establish that SPolyakEG achieves an O(1/K) residual convergence rate for monotone operators and linear convergence under strong monotonicity. Compared with PolyakEG, SPolyakEG reduces the number of operator evaluations from two to one per iteration.
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BibTeX
@misc{li2026singlecall,
title = {{Single-call Polyak-Type Extragradient Methods for Monotone Root-Finding Problems}},
author = {Keke Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05138},
eprint = {2610.05138},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05138},
}
RIS
TY - UNPB
TI - Single-call Polyak-Type Extragradient Methods for Monotone Root-Finding Problems
AU - Keke Li
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05138
UR - https://arxiv.org/abs/2610.05138
AB - We propose a single-call variant of Polyak extragradient, termed SPolyakEG, by recycling the previous extrapolation operator evaluation. Under a delayed critical condition, we establish that SPolyakEG achieves an O(1/K) residual convergence rate for monotone operators and linear convergence under strong monotonicity. Compared with PolyakEG, SPolyakEG reduces the number of operator evaluations from two to one per iteration.
ER -