arXiv:2608. 12043v1 Announce Type: cross Abstract: Acceleration for deterministic root-finding problems has been extensively studied in recent years; specifically, the anchor-based, or Halpern-type methods achieve optimal convergence rates with respect to the operator norm.
arXiv:2609.36033v1 Announce Type: cross Abstract: Among distinct optimal acceleration mechanisms for deterministic monotone root-finding problems and fixed-point problems, dual-anchoring has recently...
arXiv:2502.21099v3 Announce Type: replace-cross Abstract: This paper proposes {\sf AEPG-SPIDER}, an Adaptive Extrapolated Proximal Gradient (AEPG) method with variance reduction for minimizing compos...
arXiv:2406.02413v4 Announce Type: replace-cross Abstract: We propose a new class of fast Krasnoselkii--Mann methods with variance reduction to solve a finite-sum co-coercive equation $Gx = 0$. Our al...
arXiv:2610.07290v1 Announce Type: cross Abstract: Recent advances in penalty-based methods for stochastic bilevel optimization (SBO) have eliminated the need for second-order derivative oracles. Howe...
The paper investigates Polyak-type step-size strategies for extragradient methods applied to deterministic and stochastic monotone root-finding problems. It shows that the projection-based correction in deterministic extragradient can be derived by minimizing an upper bound on the distance to a solution, mirroring classical Polyak step-size construction. The authors provide a unified deterministic analysis that does not require global Lipschitz continuity, achieving sublinear convergence under H"older or “(L0, L1)-Lipschitz” conditions and linear convergence with strong monotonicity, and extend the approach to stochastic settings with both direct and decreasing step-size variants.
arXiv:2609. 28543v1 Announce Type: cross Abstract: We analyze a simple stochastic inertial Krasnosel'skii--Mann (iKM) method for finding a fixed point of a nonexpansive operator in a real Hilbert space.
arXiv:2508.16791v2 Announce Type: replace-cross Abstract: We develop a novel past-extragradient-type algorithmic framework, combining both Nesterov's \textit{acceleration} and \textit{variance-reduct...
The paper introduces single-loop stochastic projected damped extragradient (SPDE) and its variance-reduced variant (VR-SPDE) for stochastic nonconvex–(strongly) concave minimax problems. It provides SFO complexity bounds for achieving game stationarity and optimization stationarity, improving upon previous multi-loop methods while maintaining a single-loop structure. The results claim the best-known SFO complexities for these stationarity criteria among single-loop stochastic first‑order methods.
arXiv:2607. 09097v1 Announce Type: cross Abstract: We study stochastic fixed-point equations $\mathbf{T}(\mathbf{x}) = \mathbf{x}$ over normed spaces $(\mathcal{E}, \|\cdot\|)$, where the operator $\mathbf{T}$ is nonexpansive or contractive and is accessed only through unbiased stochastic evaluations with bounded second central moment.
arXiv:2606. 21528v2 Announce Type: replace-cross Abstract: We study first-order methods for solving monotone variational inequalities arising in min-max optimization.
arXiv:2609.09524v1 Announce Type: cross Abstract: We study the oracle complexity of computing a point with small fixed-point residual $\|T(x)-x\| \leq \epsilon$, for a general norm $\|\cdot\|$ and a...
arXiv:2607. 13414v1 Announce Type: cross Abstract: Non-expansive two-time-scale stochastic approximation is governed by a slow stochastic Krasnoselskii--Mann fixed-point iteration rather than by contraction to a unique equilibrium.