Lesi Chen

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20242026

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Showing 2026 · math.OCShow all

4 papers · 2 filters

math.OC2026

Halpern Iteration Achieves $O ~ (ε^{- 1/ p})$ $p$ 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,…

math.OC2026

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 $δ$ -inexact Hessians. We show that AINE c…

math.OC2026

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…

math.OC2026

Solving Convex-Concave Problems with $O ~ (ε^{- 4/ (3 p + 1)})$ $p$ th-Order Oracle Complexity

Lesi Chen, Xinliang Zhang, Chengchang Liu +3

When the objective has Lipschitz continuous $p$ th-order derivatives, it is known that convex-concave minimax problems can be solved with $O (ε^{- 2/ (p + 1)})$ $p$ th-order ora…

Halpern Iteration Achieves O~(ε−1/p) pth-Order Oracle Complexity for Monotone Variational Inequalities

Optimal Convex Optimization with Inexact Second-Order Oracles

Second-Order Bilevel Optimization with Accelerated Convergence Rates

Solving Convex-Concave Problems with O~(ε−4/(3p+1)) pth-Order Oracle Complexity

Halpern Iteration Achieves $O ~ (ε^{- 1/ p})$ $p$ th-Order Oracle Complexity for Monotone Variational Inequalities

Solving Convex-Concave Problems with $O ~ (ε^{- 4/ (3 p + 1)})$ $p$ th-Order Oracle Complexity