Augmented Lagrangian Method

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Overview

Augmented Lagrangian methods turn constrained optimization into a sequence of penalized problems, updating multipliers to drive solutions toward feasibility without relying on ever-larger penalties alone. Current approaches include classical multiplier updates, linearized and smoothed primal-dual methods, and inexact or matrix-free subproblem solvers, with guarantees for convex, nonconvex, stochastic, and nonsmooth settings. They are used in applications ranging from safe reinforcement learning and causal discovery to differentiable optimization and contact-rich robot planning. A central tension is balancing reliable feasibility and convergence guarantees against ill-conditioning, expensive subproblem solves, noisy constraint estimates, and constraints that may be infeasible.

Latest papers

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19 papers2 papers in the last four weeks, down 50% on the four weeks before. 0.0% of all new papers.

  1. MAGMA: Multiplier-Augmented Geometric Motion Algorithm

    Oct 15, 2026César E. Ramos Chuquiure, Vansh Thakur, Challen Enninful Adu +1Trajectory OptimizationOptimal Control

    Robotics, University of Michigan, Ann Arbor, MI

  2. LEAP: Gradient Flow Augmented Lagrangian Trajectory Optimization for Contact Constrained Robots

    Oct 14, 2026César E. Ramos Chuquiure, Ryan Tsai, Yutong Zhou +8Hypergradient OptimizationTrajectory Optimization

    Department of Robotics, University of Michigan, Ann Arbor, MI, USA. · Computer Science and Engineering, University of Michigan, Ann Arbor, MI, USA. · Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA.

  3. lapanda: A Matrix-Free Differentiable Solver for Nonconvex Constrained Optimization Layers

    Sep 27, 2026Yuankun Chen, Zifei Nie, Kangyu Lin +2Differentiable ProgrammingNonconvex Optimization

    School of Artificial Intelligence, Jilin University, China · Graduate School of Informatics, Kyoto University, JPN · Department of Civil and Systems Engineering, Johns Hopkins University, USA

  4. Scaling Laws for Physics-Aware ACOPF Surrogate Learning

    Sep 14, 2026Yijiang Li, Emon Dey, Stefano Fenu +3Neural Surrogate ModelingOptimal Power Flow

    Argonne National Laboratory Lemont, USA · Oak Ridge National Laboratory Oak Ridge, USA

  5. Equilibrium bias and convergence in augmented primal--dual dynamics with sampled constraints

    Sep 12, 2026Kang Liu, Mengxiao Chen, Siqi Xiong +1Primal-Dual OptimizationStochastic Optimization Convergence

    School of Future Technology, Xi’an Jiaotong University, Xi’an, China · School of Automation Science and Engineering, Xi’an Jiaotong University, Xi’an, China · Department of Rehabilitation Sciences, The Hong Kong Polytechnic University, Hong Kong SAR, China

  6. Guide, Not Bind: Why Defeasible Priors Fail in Augmented Lagrangian Causal Discovery

    Sep 3, 2026Sairam Sundararaman, Sara Girdhar, Manit Narasimha Murthy +2Causal DiscoveryCausal Identifiability

    Department of Computer Science (AI & ML) PES University · Department of Computer Science2026 PES University · Department of Computer Science PES University

  7. A Local-Linearly Convergent Algorithm for Nonconvex Equality-Constrained Optimization

    Aug 12, 2026Frank E. Curtis, Lingjun Guo, Daniel P. RobinsonOptimization Convergence AnalysisNonconvex Optimization

    Department of Industrial and Systems Engineering, Lehigh University

  8. Hybrid Augmented Lagrangian Method for General Constrained Optimization via Evolutionary Algorithms

    Jul 18, 2026Lampros Printzios, Konstantinos ChatzilygeroudisEvolutionary OptimizationAugmented Lagrangian Method

    Laboratory of Automation & Robotics (LAR), Department of Electrical & Computer Engineering, University of Patras, University Campus, Patras, GR-26504, Achaia, Greece

  9. Nonconvex Composite Functional Constraints via First-Order Augmented Lagrangian Methods under Local Regularity

    Jul 9, 2026Linglingzhi Zhu, Jiajin LiPrimal-Dual OptimizationNonconvex Optimization

    H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA. · Sauder School of Business, University of British Columbia, Vancouver, BC, Canada.

  10. Infeasible optimization problems and the hierarchical augmented Lagrangian method in imitation learning

    May 30, 2026Roland Andrews, Justin Carpentier, Ajay SathyaImitation LearningAugmented Lagrangian Method

  11. Augmented Lagrangian Predictive Coding

    May 29, 2026Jeffrey Seely, Julian GouldBackpropagationPredictive Coding

    Sakana AI

  12. Exploiting Non-Negativity in DAG Structure Learning

    May 19, 2026Samuel Rey, Madeline navarro, Santiago Segarra +1Graph Structure LearningStructural Causal Models

    Dept. of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA

  13. Augmented Lagrangian Method for Last-Iterate Convergence for Constrained MDPs

    May 12, 2026Michael Lu, Max Qiushi Lin, Mo Chen +1Markov Decision ProcessesLast-Iterate Convergence

    Simon Fraser University

  14. IMPACT: An Implicit Active-Set Augmented Lagrangian for Fast Contact-Implicit Trajectory Optimization

    May 9, 2026Jiayun Li, Dejian Gong, Georgia ChalvatzakiConstrained Motion PlanningTrajectory Optimization

    1PEARL Lab, Dept. of Computer Science, TU Darmstadt, Germany · 2Hessian.AI, Darmstadt, Germany · 3Robotics Institute Germany (RIG)

  15. Matrix-Valued Optimism is Matrix-Valued Augmentation: Additive Hybrid Designs for Constrained Optimization

    May 7, 2026Jiayi ZhaoPrimal-Dual OptimizationAugmented Lagrangian Method

    University of Washington Seattle, WA, USA

  16. Augmented Lagrangian Multiplier Network for State-wise Safety in Reinforcement Learning

    May 1, 2026Jiaming Zhang, Yujie Yang, Yao Lyu +2Constrained RLAugmented Lagrangian Method

    School of Vehicle and Mobility & College of AI, Tsinghua University, Beijing, 100084, China

  17. Primal-Dual Methods for Nonsmooth Nonconvex Optimization with Orthogonality Constraints

    Apr 5, 2026Linglingzhi Zhu, Wentao Ding, Shangyuan Liu +1Orthogonal OptimizationConstrained Optimization

    H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA · Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

  18. A distributed semismooth Newton based augmented Lagrangian method for distributed optimization

    Feb 27, 2026Qihao Ma, Chengjing Wang, Peipei Tang +2Distributed OptimizationAugmented Lagrangian Method

    School of Mathematics, Southwest Jiaotong University, No.999, Xian Road, West Park, High-tech Zone, Chengdu 611756, China · School of Computer and Computing Science, Hangzhou City University, Zhejiang Key Laboratory of Big Data Intelligent Computing, Hangzhou, 310015, China · Department of Control Science and Engineering, College of Electronics and Information Engineering, National Key Laboratory of Autonomous Intelligent Unmanned Systems, Tongji University, Shanghai 201804, China +1

  19. Mirror Descent Linearized Augmented Lagrangian Methods for Nonconvex Constrained Stochastic Zeroth-Order Optimization

    Apr 13, 2025Qiankun Shi, Han Yuan, Xiao Wang +1Zeroth-Order OptimizationAugmented Lagrangian Method

    Sun Yat-sen University, Guangzhou, 510006, China · Pengcheng Laboratory, Shenzhen, 518066, China · Sun Yat-sen University, Guangzhou, 518066, China +1