Quadratic Programming

Also known as QP

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Overview

Quadratic programming (QP) studies how to minimize or maximize a quadratic objective subject to constraints, commonly linear ones. It appears in robotics and control, portfolio decisions, model merging, and game-solving, where it can balance goals while enforcing safety or resource limits. Common approaches include active-set and interior-point methods, primal-dual solvers, and ADMM, with GPU acceleration, warm starts, and constraint relaxation used for large or real-time problems. A central challenge is making solvers fast and numerically reliable when problems are large, degenerate, or infeasible, without losing useful guarantees.

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. Safe Ergodic Control for Multi-Robot Systems via Quadratic Programming

    Oct 4, 2026Yo Toyomoto, Mohamed Elobaid, Bryce L. Ferguson +2Multi-Robot SystemsControl Barrier Functions

    Electrical and Computer Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia · Thayer School of Engineering at Dartmouth College, Hanover, NH, USA · Department of Computer Science, Dartmouth College, Hanover, NH, USA

  2. Efficient Reasoning via Constrained Optimization in Latent Space

    Sep 28, 2026Zhinan Hou, Xingchen Li, Keyou YouOverthinking in Language ModelsEfficient Language Model Reasoning

    Tsinghua University

  3. End-to-end QP-based policies: A unified perspective on robust control and robot learning

    Sep 25, 2026Fausto Vega, Priyanka Supraja Balaji, Chase Dunaway +3Robot Policy LearningFeedback Control

    Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, USA · Department of Mechanical Engineering, California Institute of Technology, Pasadena, CA, USA

  4. S4R: Scaling for Rigid-Body Interpenetration Resolution

    Sep 17, 2026Zhiyang Dou, Ang Zhao, Chen Peng +8Quadratic ProgrammingPhysics-Based Simulation

    Texas A&M University, College Station, USA

  5. ElastiQP: An Always-Feasible QP Solver for Constrained Robot Control

    Sep 16, 2026Daniel Morton, Jon Arrizabalaga, Zachary Manchester +1Robotic ControlConstrained Optimization

    Departments of Mechanical Engineering and Aeronautics & Astronautics, Stanford University, USA · Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, USA

  6. CALOS: Control-Affine Lyapunov On-manifold Safety Layer for Safe Deep Reinforcement Learning for Quadrotors

    Sep 15, 2026Fabrizio Cesareo, Sebastiano Mengozzi, Nicola Mimmo +1RL ControlLyapunov-Based Control

    Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi” — DEI University of Bologna, Italy

  7. WarpMPC: Large-Batch MPC on GPU via ADMM with Unrolled LDL⊤LDL^\top Factorization

    Jul 13, 2026Henrik Hose, Se Hwan Jeon, Charles Khazoom +2GPU Kernel OptimizationGPU Acceleration

    Institute for Data Science in Mechanical Engineering (DSME), RWTH Aachen University, Germany · Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge MA, USA.

  8. Elastic ODYN: Differentiable Optimization for Infeasible Control and Learning in Robotics

    Jun 15, 2026Aristotelis Papatheodorou, Jose Rojas, Ioannis Havoutis +1Robotic ControlPrimal-Dual Optimization

    Department of Engineering Science, University of Oxford, Oxford, UK · Robot Motor Intelligence (RoMI) Lab, Heriot-Watt University, Edinburgh, UK

  9. Model Merging by Output-Space Projection

    May 27, 2026Bethan Evans, Benjamin Etheridge, Stephen Roberts +1Quadratic ProgrammingLanguage Model Merging

    Department of Mathematics, University of Oxford, Oxford, UK · Department of Engineering Science, University of Oxford, Oxford, UK.

  10. Planning Smooth and Safe Control Laws for a Unicycle Robot Among Obstacles

    Apr 19, 2026Aref Amiri, Basak Sakcak, Steven M. LaValleRobotic ControlConstrained Motion Planning

    Faculty of Information Technology and Electrical Engineering, University of Oulu · Department of Advanced Computing Sciences, Maastricht University

  11. Complementarity by Construction: A Lie-Group Approach to Solving Quadratic Programs with Linear Complementarity Constraints

    Apr 13, 2026Arun L. Bishop, Micah I. Reich, Zachary ManchesterConstrained OptimizationQuadratic Programming

    Authors are with the Robotics Institute, Carnegie Mellon University · Author is with the Department of Aeronautics and Astronautics, Massachusetts Institute of Technology

  12. Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU

    Apr 8, 2026Jeffrey Fang, Glen ChouRobotic ControlNonlinear MPC

    Georgia Institute of Technology, Atlanta, GA 30308

  13. Implicit Primal-Dual Interior-Point Methods for Quadratic Programming

    Apr 1, 2026Jon Arrizabalaga, Zachary ManchesterPrimal-Dual OptimizationQuadratic Programming

    Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, USA

  14. Exploiting Low-Rank Objective Structure in Discrete Quadratic Optimization

    Feb 23, 2026Ria Stevens, Fangshuo Liao, Barbara Su +3Combinatorial OptimizationQuadratic Programming

    Rice University

  15. ODYN: An All-Shifted Non-Interior-Point Method for Quadratic Programming in Robotics and AI

    Feb 17, 2026Jose Rojas, Aristotelis Papatheodorou, Sergi Martinez +3Quadratic ProgrammingConstrained Optimization

    Robot Motor Intelligence (RoMI) Lab, Heriot-Watt University, U.K. · Oxford Robotics Institute (ORI), University of Oxford, U.K. · Humanoids and Human Centered Mechatronics, Italian Institute of Technology, Italy.

  16. Covariance-Aware Transformers for Quadratic Programming and Decision Making

    Feb 16, 2026Kutay Tire, Yufan Zhang, Ege Onur Taga +1Quadratic ProgrammingPortfolio Optimization

    The University of Texas at Austin · University of Michigan

  17. OPTIMA: Optimal One-shot Pruning for LLMs via Quadratic Programming Reconstruction

    Dec 15, 2025Mohammad Mozaffari, Samuel Kushnir, Maryam Mehri Dehnavi +1LLM PruningNeural Network Pruning

    University of Toronto · Google DeepMind

  18. ReMoSPLAT: Reactive Mobile Manipulation Control on a Gaussian Splat

    Dec 10, 2025Nicolas Marticorena, Tobias Fischer, Niko SuenderhaufRobotic ControlMobile Manipulation

    QUT Centre For Robotics, School of Electrical Engineering and Robotics at the Queensland University of Technology, Brisbane, QLD 4000, Australia

  19. Quadratic Programming Approach for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games

    Sep 30, 2025Sam GanzfriedNash EquilibriumImperfect-Information Games

    Ganzfried Research