Ling Liang

Publication

Published and accepted papers, together with preprints.

Preprints

  • Mixed-precision GPU acceleration for large-scale minimum enclosing ball problems Preprint

    Ling Liang, Lei Yang

    2026. arXiv.

    Research highlight

    GPU Computing Mixed Precision

    Low-precision screening and high-precision refinement reduce GPU work while retaining an accurate, fully checked enclosing ball.

    Runtime in seconds on a logarithmic scale for mp-ripALM, ripALM, CGAL, SCS, and CLARABEL, with 1,000 to 100,000 balls in dimension 50.
    Runtime at d = 50 for 1,000–100,000 balls. ripALM and mp-ripALM run on GPU; CGAL, SCS, and CLARABEL run on CPU.

  • A provably convergent and practical algorithm for Gromov-Wasserstein optimal transport Preprint

    Ling Liang, Lei Yang

    2026. arXiv.

    Research highlight

    Distribution Matching

    A practical inexact projected-gradient framework brings verifiable projection accuracy and convergence guarantees to Gromov–Wasserstein transport.

    Two rigidly transformed three-point spaces with equal pairwise distances, illustrating Gromov–Wasserstein matching.
    Toy spaces illustrate matching within-space geometry; the algorithm uses verifiable inexact projections.

  • Beyond expected information gain: stable Bayesian optimal experimental design with integral probability metrics and plug-and-play extensions Preprint

    Di Wu, Ling Liang, Haizhao Yang

    2026. arXiv.

    Research highlight

    Bayesian Inference

    Integral probability metrics provide stable, geometry-aware alternatives to expected information gain for Bayesian experimental design.

    Normalized preference-learning design utilities and their regions above 80 percent of peak utility.
    Preference-learning example: design regions above 80% of each utility’s own peak.

  • Fast and effective computation of generalized symmetric matrix factorization Preprint

    Lei Yang, Han Wan, Min Zhang, Ling Liang

    2026. arXiv.

    Research highlight

    Matrix Factorization Machine Learning

    Exactness results make generalized symmetric factorization amenable to the convergent A-NAUM alternating method.

    Two exactness results
    LayerWhat becomes exact
    ModelA finite quadratic penalty enforces symmetry.
    RelaxationStationary points are linked through an auxiliary-variable formulation.
    Both statements require the conditions established in the paper.

  • D-ripALM: A tuning-friendly decentralized relative-type inexact proximal augmented Lagrangian method Preprint

    Jiayi Zhu, Hong Wang, Ling Liang, Lei Yang

    2026. arXiv.

    Research highlight

    Decentralized Optimization

    Relative-error control makes decentralized ALM easier to tune, with convergence analysis covering nonsmooth, generally convex objectives.

    A decentralized network of local objectives with inexact solves and a relative-error check.
    A simplified view of the inner/outer switching rule and neighbor communication.

  • Convergence of a relative-type inexact proximal ALM for convex nonlinear programming Preprint

    Lei Yang, Jiayi Zhu, Ling Liang, Kim-Chuan Toh

    2025. arXiv.

    Research highlight

    Inexact Optimization

    A unified analysis explains the global behavior and asymptotic rates of relative-type inexact preconditioned proximal ALM.

    Convergence at three levels
    ObjectGuarantee
    IteratesGlobal convergence
    Local behaviorAsymptotic linear or superlinear rates
    Ergodic averagesObjective-residual and feasibility bounds
    Each guarantee is subject to its stated assumptions; local rate results require additional conditions.

  • PINS: Proximal iterations with sparse Newton and Sinkhorn for optimal transport Preprint

    Di Wu, Ling Liang, Haizhao Yang

    2025. arXiv.

    Research highlight

    Sparse Newton Methods

    Sparse Newton and Sinkhorn steps make entropic proximal iterations accurate and efficient, with large gains on the reported benchmarks.

    Matched-accuracy wall time (seconds)
    InstanceSinkhorn + EPPAPINS
    Synthetic, n = 40047.681.455
    MNIST, N = 224.661.66
    MNIST, N = 43,793.251.74
    Same EPPA outer iteration count and matched final accuracy. Selected rows from the paper; N is its MNIST augmentation setting.

  • ripALM: A relative-type inexact proximal augmented Lagrangian method with applications to quadratically regularized optimal transport Preprint

    Jiayi Zhu, Ling Liang, Lei Yang, and Kim-Chuan Toh

    2024. arXiv.

    Research highlight

    Optimal Transport

    One relative tolerance replaces delicate error-sequence tuning while retaining convergence guarantees for inexact proximal ALM.

    Practical relative-error control
    ComponentripALM
    Inner toleranceOne relative parameter in [0, 1)
    Tolerance sequenceNo prescribed summable sequence
    Correction stepNot required
    “One parameter” refers to the inner error criterion, not all algorithm settings.

  • PNOD: An efficient projected Newton framework for exact optimal experimental designs Preprint

    Ling Liang, Haizhao Yang

    2024. arXiv, code.

    Research highlight

    Integer Optimization

    Efficient projected Newton node solves accelerate branch-and-bound for integer A- and D-optimal experimental designs.

    A branch-and-bound tree with projected Newton continuous relaxations at its nodes.
    The schematic highlights the continuous relaxations that dominate node evaluation.

Published & Accepted Papers

  • OptimAI: Optimization from natural language using LLM-powered AI agents

    Raghav Thind, Youran Sun, Ling Liang, Haizhao Yang

    Journal of Machine Learning, accepted, 2026. JML, arXiv.

    Research highlight

    LLM Agents Automated Modeling

    Four cooperating LLM roles formulate, plan, implement, and debug optimization problems expressed in natural language.

    The OptimAI formulator, planner, coder, and code critic, including a feedback loop for code refinement.
    A simplified architecture: structured roles and iterative debugging turn descriptions into executable solutions.

  • From equations to insights: Unraveling symbolic structures in PDEs with LLMs

    Rohan Bhatnagar, Ling Liang, Krish Patel, Haizhao Yang

    SIAM Journal on Scientific Computing, accepted, 2026. SISC, arXiv.

    Research highlight

    Scientific Discovery Symbolic PDEs

    LLMs predict operators in PDE solutions, narrowing symbolic search and improving interpretable analytical approximations.

    Symbolic PDE and boundary information feeds an LLM that predicts operators for a downstream symbolic solver.
    A simplified view of operator prediction guiding symbolic solution construction.

  • Accelerating multi-block constrained optimization by learning penalty parameters

    Ling Liang, Cameron Austin, and Haizhao Yang

    Communications on Pure and Applied Analysis, accepted, 2026. CPAA, arXiv.

    Research highlight

    Learning to Optimize Constrained Optimization

    Learned penalty parameters accelerate multi-block MPALM, reducing the need for manual tuning on Lasso and optimal transport problems.

    Log-normalized MSE versus iteration for learned-penalty LMPALM and baselines on a Lasso problem with m=10 and n=20.
    Lasso example, m = 10 and n = 20: log-normalized MSE versus iterations. LMPALM uses learned penalties.

  • Fast and certifiable trajectory optimization

    Shucheng Kang, Xiaoyang Xu, Jay Sarva, Ling Liang, and Heng Yang

    in Algorithmic Foundations of Robotics XVI, Volume 1: Proceedings of the Sixteenth Workshop on the Algorithmic Foundations of Robotics, Springer Proceedings in Advanced Robotics, vol. 37, pp. 43-65, Springer, 2026. Springer, arXiv, code, Best Paper Award Finalist.

    Research highlight

    Robotics Semidefinite Optimization

    Sparse SDP relaxations and GPU computation produce practical robot trajectories with computable global-optimality certificates.

    Three optimized car back-in trajectories with successive car poses colored along each path.
    Car back-in trajectories. Across the paper’s five benchmarks, certified suboptimality is below 1%.

  • NewVEM: A Newton vertex exchange method for a class of constrained self-concordant minimization problems

    Ling Liang, Kim-Chuan Toh, and Haizhao Yang

    Journal of Scientific Computing 105, no. 64 (2025). JSC, arXiv.

    Research highlight

    Self-Concordant Optimization

    Projected Newton outside and vertex exchange inside form a fast two-level method for self-concordant optimization over generalized simplices.

    D-optimal design runtime comparison: NewVEM is faster than FWPN at all five tested sizes, from 10,000 to 50,000 candidate design points.
    D-optimal design with a quadratic/trigonometric model (p = 4). Both methods use the stopping criterion λₖ ≤ 10⁻³.

  • Nesterov's accelerated Jacobi-type methods for large-scale symmetric positive semidefinite linear systems

    Ling Liang, Qiyuan Pang, Kim-Chuan Toh, and Haizhao Yang

    SIAM Journal on Scientific Computing 47, no. 6 (2025). SISC, arXiv, code.

    Research highlight

    Linear Systems Parallel Computing

    Nesterov acceleration improves Jacobi-type convergence while preserving the simple, parallel structure of the updates.

    Parallel row-block updates feeding an accelerated Jacobi step, with an O(1/k squared) objective rate.
    The rate is for the associated convex quadratic objective, under the method’s assumptions.

  • An inexact Halpern iteration with application to distributionally robust optimization

    Ling Liang, Zusen Xu, Kim-Chuan Toh, and Jia-Jie Zhu

    Journal of Optimization Theory and Applications 260, no. 58 (2025): 1-41. JOTA, arXiv, code.

    Research highlight

    Distributionally Robust Optimization

    Inexact Halpern updates retain O(1/k) residual rates—expected residuals in the stochastic setting—and enable practical Wasserstein DRO.

    Blue empirical samples and orange worst-case perturbed samples, connected by trajectories from inexact stochastic Halpern updates.
    Empirical samples (blue) move toward worst-case perturbations (orange) in the nonlinear DRO example.

  • A squared smoothing Newton method for semidefinite programming

    Ling Liang, Defeng Sun, and Kim-Chuan Toh

    Mathematics of Operations Research 50, no. 4 (2025): 2433-3282. MOOR, arXiv.

    Research highlight

    Semidefinite Optimization

    Huber smoothing preserves zero eigenvalue contributions, allowing a squared smoothing Newton method to exploit structure in SDP.

    The positive-part function and Huber approximations for epsilon 0.25 and 0.75, all zero on negative inputs.
    Scalar Huber smoothing preserves the zero region and smooths the PSD projection when applied to eigenvalues.

  • On the stochastic (variance-reduced) proximal gradient method for regularized expected reward optimization

    Ling Liang, Haizhao Yang

    Transactions on Machine Learning Research, 2024. TMLR, arXiv.

    Research highlight

    Reinforcement Learning

    Importance-sampling-based variance reduction improves sample complexity for general regularized expected-reward optimization.

    Samples to reach ε-stationarity
    MethodSample complexity
    Stochastic proximal gradientO(ε⁻⁴)
    Variance-reduced proximal gradient with PAGEO(ε⁻³)
    Bounds hold under the respective assumptions; the improved rate uses additional conditions.

  • A sparse smoothing Newton method for solving discrete optimal transport problems

    Di Hou, Ling Liang, and Kim-Chuan Toh

    ACM Transactions on Mathematical Software 50, no. 3 (2024): 1-26. TOMS, arXiv.

    Research highlight

    Newton Methods

    A Huber-based Newton method exploits sparse transport solutions to reduce computation and memory for OT and fixed-support Wasserstein barycenters.

    A schematic sparse transport-plan pattern feeding a sparse smoothing Newton solve.
    The matrix shows an illustrative sparsity pattern, not a measured transport plan.

  • A corrected inexact proximal augmented Lagrangian method with a relative error criterion for a class of group-quadratic regularized optimal transport problems

    Lei Yang, Ling Liang, Hong T.M. Chu, and Kim-Chuan Toh

    Journal of Scientific Computing 99, no. 79 (2024). JSC, arXiv.

    Research highlight

    Inexact Optimization

    A single relative tolerance makes corrected proximal ALM with semismooth Newton subsolves practical for group-quadratic regularized transport.

    Unregularized and group-quadratic regularized transport solutions with their transport matrices inset.
    Left: λ₁ = λ₂ = 0. Right: λ₁ = λ₂ = 1. Regularization changes the structure of the transport plan.

  • Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decomposition

    Ching-pei Lee, Ling Liang, Tianyun Tang, and Kim-Chuan Toh

    Journal of Machine Learning Research 25, no. 379 (2024): 1-52. JMLR, arXiv, code.

    Research highlight

    Low-Rank Optimization Machine Learning

    Cheap factorized steps gain the safeguards of convex optimization, while the algorithm adjusts the factorization rank automatically.

    Low-rank Burer–Monteiro steps alternate with aperiodic proximal safeguards and rank adaptation.
    The schematic separates the fast factorized phase from the global-convergence safeguard.

  • An inexact projected gradient method with rounding and lifting by nonlinear programming for solving rank-one semidefinite relaxation of polynomial optimization

    Heng Yang, Ling Liang, Luca Carlone, and Kim-Chuan Toh

    Mathematical Programming 201, no. 1-2 (2023): 409-472. MP, arXiv, code.

    Research highlight

    Robotics Semidefinite Optimization

    Safeguarded low-rank local search accelerates a globally convergent SDP method, combining fast nonconvex steps with convex guarantees.

    A polynomial objective and its SDP relaxation connected by rounding and lifting, with projected descent steps.
    The paper’s univariate example explains how rounding, local search, lifting, and SDP descent work together.

  • An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems

    Hong T.M. Chu, Ling Liang, Kim-Chuan Toh, and Lei Yang

    Computational Optimization and Applications 85, no. 1 (2023): 107-146. COAP, arXiv, code.

    Research highlight

    Linear Programming

    Checkable inexact stopping rules make entropic proximal iterations practical for structured LPs, including capacity-constrained multi-marginal transport.

    Runtime in seconds for iEPPA and Gurobi on ten three-marginal transport problems, with n = 50 times the instance ID. iEPPA takes less time across the tested sizes.
    Three-marginal capacity-constrained transport, n = 50 × id.

  • QPPAL: A two-phase proximal augmented Lagrangian method for high dimensional convex quadratic programming problems

    Ling Liang, Xudong Li, Defeng Sun, and Kim-Chuan Toh

    ACM Transactions on Mathematical Software 48, no. 3 (2022): 1-27. TOMS, arXiv, code.

    Research highlight

    Quadratic Programming

    A two-phase solver pairs inexpensive warm-start iterations with accurate proximal ALM refinement for high-dimensional convex QP.

    QPPAL phase I uses symmetric Gauss–Seidel updates and phase II refines the solution with proximal ALM.
    Phase I targets low-to-medium accuracy; Phase II efficiently refines the warm start.

  • On degenerate doubly nonnegative projection problems

    Ying Cui, Ling Liang, Defeng Sun, and Kim-Chuan Toh

    Mathematics of Operations Research 47, no. 3 (2022): 2219-2239. MOOR, arXiv.

    Research highlight

    Conic Optimization

    Augmented Lagrangian subproblems overcome the singular Newton systems that make degenerate doubly nonnegative projection difficult.

    Handling degenerate DNN projection
    ApproachNewton equations
    Direct KKT solveThe Jacobian can be singular under degeneracy.
    Augmented LagrangianA sequence of better-conditioned nonsmooth equations.
    The DNN cone combines positive semidefiniteness with entrywise nonnegativity.

  • A new homotopy proximal variable-metric framework for composite convex minimization

    Quoc Tran-Dinh, Ling Liang, and Kim-Chuan Toh

    Mathematics of Operations Research 47, no. 1 (2022): 508-539. MOOR, arXiv.

    Research highlight

    Statistical Estimation

    A homotopy parameterization and primal-dual-primal construction preserve useful regularizer structure in proximal Newton subproblems.

    A primal problem is dualized, treated with homotopy proximal Newton, and its subproblem is solved back in primal space.
    In the covariance-estimation specialization, the method avoids matrix inversion and Cholesky factorization.

  • An inexact augmented Lagrangian method for second-order cone programming with applications

    Ling Liang, Defeng Sun, and Kim-Chuan Toh

    SIAM Journal on Optimization 31, no. 3 (2021): 1748-1773. SIOPT, arXiv.

    Research highlight

    Conic Optimization

    Quadratic-growth conditions connect SOCP geometry to fast ALM residual convergence and an effective solver for structured cone problems.

    A second-order cone beside the implication from quadratic growth to R-superlinear ALM residual convergence.
    The convergence implication holds under the regularity conditions established in the paper.