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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…
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…
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…
FMIP: Joint Continuous-Integer Flow For Mixed-Integer Linear Programming
Hongpei Li, Hui Yuan, Han Zhang +4
Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challe…
PDHCG: A Scalable First-Order Method for Large-Scale Competitive Market Equilibrium Computation
Huikang Liu, Yicheng Huang, Hongpei Li +2
Large-scale competitive market equilibrium problems arise in a wide range of important applications, including economic decision-making and intelligent manufacturing. Traditional s…
A Practical GPU-Enhanced Matrix-Free Primal-Dual Method for Large-Scale Conic Programs
Zhenwei Lin, Zikai Xiong, Dongdong Ge +1
In this paper, we introduce a practical GPU-enhanced matrix-free first-order method for solving large-scale conic programming problems, which we refer to as PDCS, standing for the…
Accelerating Low-Rank Factorization-Based Semidefinite Programming Algorithms on GPU
Qiushi Han, Zhenwei Lin, Hanwen Liu +4
In this paper, we address a long-standing challenge: how to achieve both efficiency and scalability in solving semidefinite programming problems. We propose breakthrough accelerati…
A Single-Loop Robust Policy Gradient Method for Robust Markov Decision Processes
Zhenwei Lin, Chenyu Xue, Qi Deng +1
Robust Markov Decision Processes (RMDPs) have recently been recognized as a valuable and promising approach to discovering a policy with creditable performance, particularly in the…
Restarted Primal-Dual Hybrid Conjugate Gradient Method for Large-Scale Quadratic Programming
Yicheng Huang, Wanyu Zhang, Hongpei Li +3
Convex quadratic programming (QP) is an essential class of optimization problems with broad applications across various fields. Traditional QP solvers, typically based on simplex o…
A Low-Rank ADMM Splitting Approach for Semidefinite Programming
Qiushi Han, Chenxi Li, Zhenwei Lin +5
We introduce a new first-order method for solving general semidefinite programming problems, based on the alternating direction method of multipliers (ADMM) and a matrix-splitting…
cuPDLP-C: A Strengthened Implementation of cuPDLP for Linear Programming by C language
Haihao Lu, Jinwen Yang, Haodong Hu +6
A recent GPU implementation of the Restarted Primal-Dual Hybrid Gradient Method for Linear Programming was proposed in Lu and Yang (2023). Its computational results demonstrate the…
Beyond Nonconvexity: A Universal Trust-Region Method with New Analyses
Yuntian Jiang, Chang He, Chuwen Zhang +3
The trust-region (TR) method is renowned historically for its robustness in nonconvex problems and extraordinary numerical performance, but the study of its performance in convex o…
Trust Region Methods For Nonconvex Stochastic Optimization Beyond Lipschitz Smoothness
Chenghan Xie, Chenxi Li, Chuwen Zhang +3
In many important machine learning applications, the standard assumption of having a globally Lipschitz continuous gradient may fail to hold. This paper delves into a more general…