Lesi Chen

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20242026

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5 papers · 1 filter

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…

math.OC2025

Faster Gradient Methods for Highly-Smooth Stochastic Bilevel Optimization

Lesi Chen, Junru Li, El Mahdi Chayti +1

This paper studies the complexity of finding an $ε$ -stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is st…

math.OC2025

Solving Convex-Concave Problems with $O ~ (ε^{- 4/7})$ Second-Order Oracle Complexity

Lesi Chen, Chengchang Liu, Luo Luo +1

Previous algorithms can solve convex-concave minimax problems $min_{x \in X} max_{y \in Y} f (x, y)$ with $O (ε^{- 2/3})$ second-order oracle calls usin…

math.OC2024

Second-Order Min-Max Optimization with Lazy Hessians

Lesi Chen, Chengchang Liu, Jingzhao Zhang

This paper studies second-order methods for convex-concave minimax optimization. Monteiro and Svaiter (2012) proposed a method to solve the problem with an optimal iteration comple…

math.OC2024

Functionally Constrained Algorithm Solves Convex Simple Bilevel Problems

Huaqing Zhang, Lesi Chen, Jing Xu +1

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundament…