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Stochastic Gradient Methods with Online Scaling
Wanyu Zhang, Wenzhi Gao, Yinyu Ye +1
This paper introduces Stochastic Online Scaled Gradient Methods (SOSGM), a generalization of the recently developed adaptive preconditioning framework in arXiv:2505.23081 and arXiv…
Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp
Wenzhi Gao, Zhaonan Qu, Yinyu Ye +1
We revisit the Sinkhorn-Knopp (SK) algorithm for the matrix scaling problem. Despite extensive literature on the global convergence of SK and its variants, its local linear converg…
GPU-Accelerated Conic Quadratic Programming with Local Linear Convergence under Strict Complementarity
Hongpei Li, Yicheng Huang, Huikang Liu +2
We present PDHCG-CQP, a GPU-accelerated first-order solver for large-scale conic convex quadratic programming. PDHCG-CQP supports affine constraints and Cartesian products of nonne…
A Curvature-Aware Rank-Adaptive Distributed Augmented-Lagrangian Solver for Large-Scale SDPs
Hongpei Li, Huikang Liu, Dongdong Ge +1
We present CARDAL (Curvature-Aware Rank-Adaptive Distributed Augmented Lagrangian), a distributed multi-GPU solver for large-scale semidefinite programs (SDPs) based on a rank-adap…
The Simple Strategy-Iteration Method is Strongly Polynomial for the Turn-Based Deterministic Forward Game
Sanyou Mei, Chunlin Sun, Yinyu Ye
We study Turn-Based Deterministic Forward Games (TBDFGs), the subclass of turn-based deterministic zero-sum games in which no directed cycle contains actions controlled by both pla…
OR-Space: A Full-Lifecycle Workspace Benchmark for Industrial Optimization Agents
Chenyu Zhou, Xinyun Lu, Jiangyue Zhao +3
Large language model (LLM) agents are increasingly used to assist with operations research (OR) modeling, yet existing OR-oriented benchmarks often reduce evaluation to one-shot tr…
OSDN: Improving Delta Rule with Provable Online Preconditioning in Linear Attention
Chenyu Zhou, Hongpei Li, Yuerou Liu +3
Linear attention and state-space models offer constant-memory alternatives to softmax attention, but often struggle with in-context associative recall. The Delta Rule mitigates thi…
A Technical Note on the Implementation and Use of PDCS
Zhenwei Lin, Zikai Xiong, Dongdong Ge +1
This technical note documents the implementation and use of the Primal-Dual Conic Programming Solver (PDCS), a first-order solver for large-scale conic optimization problems introd…
A Single-Sample Polylogarithmic Regret Bound for Nonstationary Online Linear Programming
Haoran Xu, Owen Shen, Peter Glynn +2
We study nonstationary Online Linear Programming (OLP), where orders arrive sequentially with reward-resource consumption pairs that form a sequence of independent, but not nec…
PDHCG-II: An Enhanced Version of PDHCG for Large-Scale Convex QP
Hongpei Li, Yicheng Huang, Huikang Liu +2
Quadratic programming (QP) is a fundamental optimization model with wide-ranging applications in decision-making and machine learning, yet efficiently solving large-scale instances…
D-PDLP: Scaling PDLP to Distributed Multi-GPU Systems
Hongpei Li, Yicheng Huang, Huikang Liu +2
We present a distributed framework of the Primal-Dual Hybrid Gradient (PDHG) algorithm for solving massive-scale linear programming (LP) problems. Although PDHG-based solvers demon…