2 citations · 3 across the 18 of their papers we have counts for
18 papers
On the Local Linear Convergence of Operator Splitting Methods for Conic Programming
Lijun Ding, Haihao Lu, Jinwen Yang
Operator-splitting methods such as the primal-dual hybrid gradient method (PDHG) and the alternating direction method of multipliers (ADMM) often exhibit linear convergence on coni…
On the Complexity of BFGS Method for Smooth Convex Optimization
Lijun Ding, Jinwen Yang, Baoyu Zhou
We study the BFGS method with an Armijo-Wolfe line search for minimizing convex functions with Lipschitz-continuous gradients, without assuming strong convexity. We establish a glo…
FlashFolio: A GPU-Accelerated Solver for Portfolio Optimization
Yilun Jiang, Haihao Lu, Zedong Peng +1
We present FlashFolio, a GPU-accelerated solver for single-period and multi-period portfolio optimization with factor-based risk modeling, bid-offer spread costs, and nonlinear mar…
Active set identification and rapid convergence for degenerate primal-dual problems
Mateo Díaz, Pedro Izquierdo Lehmann, Haihao Lu +1
Primal-dual methods for solving convex optimization problems with functional constraints often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at…
cuPDLPx: A Further Enhanced GPU-Based First-Order Solver for Linear Programming
Haihao Lu, Zedong Peng, Jinwen Yang
We introduce cuPDLPx, a further enhanced GPU-based first-order solver for linear programming. Building on the recently developed restarted Halpern PDHG for LP, cuPDLPx incorporates…
An Overview of GPU-based First-Order Methods for Linear Programming and Extensions
Haihao Lu, Jinwen Yang
The rapid progress in GPU computing has revolutionized many fields, yet its potential in mathematical programming, such as linear programming (LP), has only recently begun to be re…
New Understandings and Computation on Augmented Lagrangian Methods for Low-Rank Semidefinite Programming
Lijun Ding, Haihao Lu, Jinwen Yang
Augmented Lagrangian Method (ALM) combined with Burer-Monteiro (BM) factorization, dubbed ALM-BM, offers a powerful approach for solving large-scale low-rank semidefinite programs…
MPAX: Mathematical Programming in JAX
Haihao Lu, Zedong Peng, Jinwen Yang
We present MPAX (Mathematical Programming in JAX), an open-source first-order solver for large-scale linear programming (LP) and convex quadratic programming (QP) built natively in…
PDOT: a Practical Primal-Dual Algorithm and a GPU-Based Solver for Optimal Transport
Haihao Lu, Jinwen Yang
In this paper, we propose a practical primal-dual algorithm with theoretical guarantees and develop a GPU-based solver, which we dub PDOT, for solving large-scale optimal transport…
Restarted Halpern PDHG for Linear Programming
Haihao Lu, Jinwen Yang
In this paper, we propose and analyze a new matrix-free primal-dual algorithm, called restarted Halpern primal-dual hybrid gradient (rHPDHG), for solving linear programming (LP). W…
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…
cuPDLP.jl: A GPU Implementation of Restarted Primal-Dual Hybrid Gradient for Linear Programming in Julia
Haihao Lu, Jinwen Yang
In this paper, we provide an affirmative answer to the long-standing question: Are GPUs useful in solving linear programming? We present cuPDLP.jl, a GPU implementation of restarte…
A Practical and Optimal First-Order Method for Large-Scale Convex Quadratic Programming
Haihao Lu, Jinwen Yang
Convex quadratic programming (QP) is an important class of optimization problem with wide applications in practice. The classic QP solvers are based on either simplex or barrier me…
On the Geometry and Refined Rate of Primal-Dual Hybrid Gradient for Linear Programming
Haihao Lu, Jinwen Yang
We study the convergence behaviors of primal-dual hybrid gradient (PDHG) for solving linear programming (LP). PDHG is the base algorithm of a new general-purpose first-order method…
On a Unified and Simplified Proof for the Ergodic Convergence Rates of PPM, PDHG and ADMM
Haihao Lu, Jinwen Yang
We present a unified viewpoint of proximal point method (PPM), primal-dual hybrid gradient (PDHG) and alternating direction method of multipliers (ADMM) for solving convex-concave…
On the Infimal Sub-differential Size of Primal-Dual Hybrid Gradient Method and Beyond
Haihao Lu, Jinwen Yang
Primal-dual hybrid gradient method (PDHG, a.k.a. Chambolle and Pock method) is a well-studied algorithm for minimax optimization problems with a bilinear interaction term. Recently…
A -Symmetric Quasi-Newton Method for Minimax Problems
Azam Asl, Haihao Lu, Jinwen Yang
Minimax problems have gained tremendous attentions across the optimization and machine learning community recently. In this paper, we introduce a new quasi-Newton method for minima…
Nearly Optimal Linear Convergence of Stochastic Primal-Dual Methods for Linear Programming
Haihao Lu, Jinwen Yang
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sha…