10 papers · 1 filter
Randomized Quasi-Gauss--Newton Methods for Solving General Nonlinear Equations
Chengchang Liu, Luo Luo
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 matri…
Halpern Iteration Achieves th-Order Oracle Complexity for Monotone Variational Inequalities
Lesi Chen, Xinliang Zhang, Hengyu Wang +3
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,…
Optimal Convex Optimization with Inexact Second-Order Oracles
Lesi Chen, Chengchang Liu, Luo Luo +2
In this paper, we present a novel second-order method called Accelerated Inexact Newton Extragradient (AINE) for convex optimization using -inexact Hessians. We show that AINE c…
Stochastic Non-Smooth Non-Convex Optimization with Decision-Dependent Distributions
Chengchang Liu, Zongqi Wan, Haishan Ye +1
We study stochastic zeroth-order optimization with decision-dependent distributions, where the sampling law depends on the current decision and only noisy function values are avail…
Second-Order Bilevel Optimization with Accelerated Convergence Rates
Sheng Yang, Chengchang Liu, Lesi Chen +1
This paper studies second-order methods for nonconvex-strongly-convex bilevel optimization. We propose a novel fully second-order bilevel approximation method (FSBA) that achieves…
Solving Convex-Concave Problems with th-Order Oracle Complexity
Lesi Chen, Xinliang Zhang, Chengchang Liu +3
When the objective has Lipschitz continuous th-order derivatives, it is known that convex-concave minimax problems can be solved with th-order ora…