This paper considers the local convergence for solving general nonlinear equations. We establish randomized quasi-Gauss--Newton methods based on the approximation of the Gram matrix, addressing both the underdetermined and the overdetermined settings. For the underdetermined case, we show that our methods achieve local...
We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI). Monteiro and Svaiter (SIAM J. Optim., 2012) showed that a second-order method, NPE, converges at a rate of $\mathcal{O}(T^{-1.5})$. For convex-concave minimax optimization, a subclass of MVI problems, Chen, Liu, Luo, a...
Xin-Liang Zhang, Le-Si Chen, Lin-Xuan Pan et al.· 1 citation
By using a large-step inexact Halpern iteration, a novel Halpern-NPE method is proposed that achieves an even faster rate of $\tilde{\mathcal{O}}(T^{-2})$ for solving MVIs and improves all prior results for $p \ge 2$ and matches the classical extragradient method for p=1.
Le-Si Chen, Xin-Liang Zhang, He Wang et al.· 0 citations
This work proposes LoRA-NSGDM, which finds an $\epsilon$-stationary point with $\mathcal{O}(\epsilon^{-8})$ stochastic oracle complexity, and LoRA-STORM, which improves the stochastic oracle complexity to $\mathcal{O}(\epsilon^{-6})$.
Ru Wang, Chengchang Liu, John C. S. Lui· arXiv.org· 1 citation
This paper shows that AINE can find an $\epsilon$-solution in the inexact second-order oracle (ISO) complexity of $\delta/\epsilon)^{1/2} + (L_2/\epsilon)^{2/7} )$ when the Hessian is $L_2$-Lipschitz continuous, and establishes matching oracle complexity lower bounds for both setups.
Lesi Chen, Chengchang Liu, Luo Luo et al.· 1 citation
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