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...
By TaeHo Yoon, Nicolas Loizou
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...
By Ganzhao Yuan
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...
By Quoc Tran-Dinh
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...
By Xingyu Chen, Ming Yang, Quanqi Hu, Tianbao Yang
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.
By TaeHo Yoon, Sayantan Choudhury, Ezra Greenberg, Nicolas Loizou
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.
By Tong Yang, Tao Jiang, Yuejie Chi, Ashok Cutkosky, Lin Xiao