Polyak-Type Extragradient Methods for Monotone Root-Finding Problems
We study Polyak-type step-size selection for extragradient methods for solving deterministic and stochastic monotone root-finding problems. We show that the known projection-type correction for deterministic extragradient arises from minimizing an upper bound on the distance to a solution, paralleling the classical Polyak step-size construction. Using this viewpoint, we provide a unified deterministic analysis of the Polyak-type Extragradient Method (PolyakEG), based on a local critical condition controlling the variation of operator $F$ along the extrapolation direction. This analysis does not require global Lipschitz continuity, and covers sublinear convergence under broader conditions ...
| Authors | TaeHo Yoon, Sayantan Choudhury, Ezra Greenberg et al. |
|---|---|
| Primary category | math.OC |
| Published | 22 September 2026 |
| Last updated at source | 22 September 2026 |
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