Luo Luo

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20242026

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5 papers · 1 filter

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.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.OC2025

Faster Newton Methods for Convex and Nonconvex Optimization in Gradient Complexity

Lesi Chen, Chengchang Liu, Luo Luo +1

Second-order optimization methods are computationally expensive for large-scale problems. Recently, Doikov, Chayti, and Jaggi (ICML 2023) proposed the LazyCRN method that reduces c…

math.OC2024

An Enhanced Levenberg--Marquardt Method via Gram Reduction

Chengchang Liu, Luo Luo, John C. S. Lui

This paper studied the problem of solving the system of nonlinear equations $F (x) = 0$ , where $F : R^{d} \to R^{d}$ . We propose Gram-Reduced Lev…

math.OC2024

On the Complexity of Finite-Sum Smooth Optimization under the Polyak-Łojasiewicz Condition

Yunyan Bai, Yuxing Liu, Luo Luo

This paper considers the optimization problem of the form $min_{x \in R^{d}} f (x) ≜ \frac{1}{n} \sum_{i = 1}^{n} f_{i} (x)$ , where $f (\cdot)$ satisfies the…

Optimal Convex Optimization with Inexact Second-Order Oracles

Solving Convex-Concave Problems with O~(ε−4/7) Second-Order Oracle Complexity

Faster Newton Methods for Convex and Nonconvex Optimization in Gradient Complexity

An Enhanced Levenberg--Marquardt Method via Gram Reduction

On the Complexity of Finite-Sum Smooth Optimization under the Polyak-Łojasiewicz Condition

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