Constrained Optimization

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Overview

The field studies how to optimize an objective over a feasible set, from convex programs and combinatorial problems to nonconvex models with complex or conflicting constraints. Classical approaches include projection and Frank–Wolfe methods, interior-point and augmented-Lagrangian algorithms, and evolutionary search; newer work also learns feasible solutions or uses neural projections and solver warm starts. Applications range from robotic trajectory planning and power-grid operation to fair machine learning, resource allocation, and scheduling. A central challenge is balancing scalable computation with reliable feasibility and convergence guarantees, especially for nonconvex or infeasible problems and settings without standard regularity conditions.

Latest papers

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337 papers40 papers in the last four weeks, up 29% on the four weeks before. 0.2% of all new papers.

  1. Towards Efficient Constraint Handling in Neural Solvers for Routing Problems

    Feb 17, 2026Jieyi Bi, Zhiguang Cao, Jianan Zhou +5Neural Combinatorial OptimizationConstrained Optimization

    Nanyang Technological University · MIT · Singapore Management University +2

  2. 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.

  3. Spatially-Aware Adaptive Trajectory Optimization with Controller-Guided Feedback for Autonomous Racing

    Feb 17, 2026Alexander Wachter, Alexander Willert, Marc-Philip Ecker +1Trajectory OptimizationAutonomous Racing

    Automation & Control Institute (ACIN), TU Wien, Vienna, Austria · AIT, Austrian Institute of Technology GmbH, Vienna, Austria

  4. Multi-Objective Coverage via Constraint Active Search

    Feb 17, 2026Zakaria Shams Siam, Xuefeng Liu, Chong LiuConstrained Optimization

    University at Albany, State University of New York, Albany, United States · University of Chicago, Chicago, United States

  5. Decision Making under Imperfect Recall: Algorithms and Benchmarks

    Feb 16, 2026Emanuel Tewolde, Brian Hu Zhang, Ioannis Anagnostides +2Sequential Decision MakingRegret Minimization

    Computer Science Dept., Carnegie Mellon University, Pittsburgh, USA · Foundations of Cooperative AI Lab (FOCAL) · Strategy Robot, Inc.; Strategic Machine, Inc.; and Optimized Markets, Inc.

  6. An Embarrassingly Simple Way to Optimize Orthogonal Matrices at Scale

    Feb 16, 2026Adrián Javaloy, Antonio VergariOrthogonal OptimizationMatrix Optimization

    Institute for Machine Learning, University of Edinburgh, GB.

  7. Truly Adapting to Adversarial Constraints in Constrained MABs

    Feb 16, 2026Francesco Emanuele Stradi, Kalana Kalupahana, Matteo Castiglioni +2Constrained OptimizationAdversarial Bandits

    Politecnico di Milano

  8. Learning to Control: The iUzawa-Net for Nonsmooth Optimal Control of Linear PDEs

    Feb 12, 2026Yongcun Song, Xiaoming Yuan, Hangrui Yue +1Optimal ControlConstrained Optimization

    Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore. · Department of Mathematics, The University of Hong Kong, Pok Fu Lam, Hong Kong SAR, China. · School of Mathematical Sciences, Nankai University, Tianjin 300071, China.

  9. Meta-Learning-Assisted Constraint Relaxation for Constrained Black-Box Optimization

    Jan 31, 2026Sijie Ma, Zeyuan Ma, Yue-Jiao Gong +1Black-Box OptimizationLearning to Optimize

    Hong Kong Polytechnic University · South China Normal University · South China University of Technology

  10. Unrolled Neural Networks for Constrained Optimization

    Jan 24, 2026Samar Hadou, Alejandro RibeiroConstrained OptimizationLearning to Optimize

    Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104 USA

  11. A Constrained Optimization Perspective of Unrolled Transformers

    Jan 24, 2026Javier Porras-Valenzuela, Samar Hadou, Alejandro RibeiroDeep Learning OptimizationTransformer

    Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, United States of America.

  12. Learning to Optimize by Differentiable Programming

    Jan 23, 2026Liping Tao, Xindi Tong, Chee Wei TanPrimal-Dual OptimizationLearning to Optimize

    Nanyang Technological University, Singapore · Nanyang Technological University, Singapore, Singapore

  13. Refined Gradient-Based Temperature Optimization for the Replica-Exchange Monte-Carlo Method

    Jan 20, 2026Tatsuya Miyata, Shunta Arai, Satoshi TakabeParallel TemperingConstrained Optimization

    Institute of Science Tokyo, Ookayama, Tokyo 152-8550, Japan

  14. Decoupling Constraints from Two Directions for Evolutionary Constrained Multi-objective Optimization

    Dec 30, 2025Ruiqing Sun, Dawei Feng, Xing Zhou +6Evolutionary OptimizationMulti-Objective Evolutionary Optimization

    College of Computer Science and Technology, National University of Defense Technology, Changsha 410000, P.R. China · College of Intelligence Science and Technology, National University of Defense Technology, Changsha, 410000, P.R. China · State Key Laboratory of Complex & Critical Software Environment, College of Information and Communication, National University of Defense Technology, Wuhan 430019, P.R. China +1

  15. Critical Points of Degenerate Metrics on Algebraic Varieties: A Tale of Overparametrization

    Dec 24, 2025Giovanni Luca Marchetti, Erin Connelly, Paul Breiding +1Constrained OptimizationOverparameterization

    KTH Royal Institute of Technology & Digital Futures

  16. Anytime-Feasible First-Order Optimization via Safe Sequential QCQP

    Nov 24, 2025Jiarui Wang, Mahyar FazlyabConstrained OptimizationNonconvex Optimization

    Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD 21218 USA

  17. Accelerated Frank-Wolfe Algorithms: Complementarity Conditions and Sparsity

    Nov 4, 2025Dan GarberConstrained OptimizationFrank-Wolfe Algorithms

    Faculty of Data and Decision Sciences Technion - Israel Institute of Technology

  18. Disciplined Biconvex Programming

    Nov 3, 2025Hao Zhu, Joschka BoedeckerNonconvex OptimizationConstrained Optimization

    IMBIT//BrainLinks-BrainTools · Department of Computer Science, University of Freiburg

  19. Smooth Quasar-Convex Optimization with Constraints

    Oct 2, 2025David Martínez-RubioRiemannian OptimizationNonconvex Optimization

    IMDEA Software Institute · Madrid, Spain

  20. MAD-PINN: A Decentralized Physics-Informed Machine Learning Framework for Safe and Optimal Multi-Agent Control

    Sep 28, 2025Manan Tayal, Aditya Singh, Shishir Kolathaya +1Multi-Agent ControlConstrained Optimization

    Center for Cyber-Physical Systems, Indian Institute of Science, Bangalore, India · Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, USA · Department of Aeronautics and Astronautics, Stanford University, USA

  21. Beyond Slater's Condition in Online CMDPs with Stochastic and Adversarial Constraints

    Sep 24, 2025Francesco Emanuele Stradi, Eleonora Fidelia Chiefari, Matteo Castiglioni +2Markov Decision ProcessesConstrained RL

    Politecnico di Milano

  22. Solving Conic Programs over Sparse Graphs using a Variational Quantum Approach: The Case of the AC Optimal Power Flow

    Aug 30, 2025Thinh Viet Le, Mark M. Wilde, Vassilis KekatosOptimal Power FlowConstrained Optimization

    Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47906, USA · School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA

  23. Efficiency, Feasibility, and Incentive-Awareness in Constrained Online Resource Allocation

    Jul 13, 2025Yan Dai, Negin Golrezaei, Patrick JailletGame TheoryOnline Convex Optimization

    Operations Research Center, MIT. · Sloan School of Management, MIT. · Department of EECS, MIT.

  24. Private Rate-Constrained Optimization with Applications to Fair Learning

    May 28, 2025Mohammad Yaghini, Tudor Cebere, Michael Menart +2Primal-Dual OptimizationGroup Fairness

    University of Toronto · Vector Institute · PreMeDICaL team +3

  25. Plan-Driven Adaptive Bidding for First-Price Auctions with Budget Constraints under Nonstationarity

    May 5, 2025Yige Wang, Jiashuo JiangPrimal-Dual OptimizationAutomated Bidding

    Department of Industrial Engineering & Decision Analytics, Hong Kong University of Science and Technology

  26. Minimisation of Quasar-Convex Functions Using Random Zeroth-Order Oracles

    May 4, 2025Amir Ali Farzin, Yuen-Man Pun, Philipp Braun +1Zeroth-Order OptimizationConstrained Optimization

    School of Engineering Australian National University · Department of Electrical and Electronic Engineering University of Melbourne · Department of Electrical and Electronic Engineering22 University of Melbourne

  27. 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

  28. Optimization on the Oblique Manifold for Sparse Simplex Constraints via Multiplicative Updates

    Mar 31, 2025Flavia Esposito, Andersen AngRiemannian OptimizationConstrained Optimization

    Department of Mathematics, University of Bari Aldo Moro, Bari, 70125, Italy. · School of Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, United Kingdom.

  29. Exploiting Concavity Information in Gaussian Process Contextual Bandit Optimization

    Mar 13, 2025Kevin Li, Eric LaberContextual BanditsGaussian Process Bandits

  30. Decentralized Projection-free Online Upper-Linearizable Optimization with Applications to DR-Submodular Optimization

    Jan 30, 2025Yiyang Lu, Mohammad Pedramfar, Vaneet AggarwalSubmodular OptimizationOnline Convex Optimization

    Purdue University, West Lafayette, IN, USA · Mila - Quebec AI Institute/McGill University, Montreal, QC, Canada