Constrained Optimization

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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

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

ML-OPF-Bench: Benchmarking Machine Learning for Optimal Power Flow
Oct 3, 2026Xinyi Liu, Xuan He, Danny H. K. Tsang +1Optimal Power Flow Learning to Optimize
Dartmouth College · Hong Kong University of Science and Technology (Guangzhou) · University of Alberta
$\tilde{O}(\sqrt{T})$ Regret and Polylogarithmic Constraint Violation for COCO
Oct 2, 2026Dhruv Sarkar, Abhishek SinhaOnline Convex Optimization Constrained Optimization
MIT Cambridge, USA · Tata Institute of Fundamental Research Mumbai, India
DePICT: Decision-Preserving Interface for Constrained Downstream Tasks
Oct 2, 2026Utkarsh Grover, Ravi Ranjan, Agoritsa Polyzou +4Predict-Then-Optimize Constrained Optimization
University of South Florida · Florida International University · DEVCOM Army Research Lab
A hybrid CNN-adjoint optimization framework for reconstruction of viscoelastic tissue properties in magnetic resonance elastography
Oct 2, 2026Anwesa Dey, Johann Rudi, Elena CherkaevImage Inverse Problems Magnetic Resonance Imaging
Department of Mathematics, The University of Utah, address USA. · Department of Mathematics, Virginia Tech, address USA. · Department of Mathematics, The University of Utah, address, address, USA.
Cross-entropy optimization with prioritized constraints
Oct 1, 2026Francisco Roldan Sanchez, Pau de las Heras Molins, David Fridovich-Keil +1Constrained Motion Planning Black-Box Optimization
LTCI, Télécom Paris, Institut Polytechnique de Paris · The University of Texas at Austin
Fixing a Model That Learned Worse Cancer Means Lower Risk: Monotonic Constraints in Bladder Cancer Recurrence Prediction
Oct 1, 2026Saram Abbas, David Thomas, Naeem Soomro +3Counterfactual Evaluation Gradient-Boosted Decision Trees
School of Engineering, Newcastle University, Newcastle upon Tyne, UK · Electronics and Computer Science, University of Southampton, Southampton, UK · Department of Urology, Freeman Hospital, Newcastle upon Tyne, UK +1
A Simple Doxastic Deontic Logic for Norm-Guided Decision Making
Sep 30, 2026Thorsten Engesser, Agata CiabattoniLogical Reasoning Constrained Optimization
TU Wien
Autoresearch in Mixed-Integer Linear and Nonlinear Programming
Sep 30, 2026Yuwei Gu, Yaoxin Wu, Tong Guo +2Automated Algorithm Discovery Mixed-Integer Linear Programming
Chengdu University of Information Technology · Eindhoven University of Technology · Nanyang University of Technology +2
Generalized Geometry Block Proximal Linearized Method for Multiblock Nonconvex and Nonsmooth Optimization
Sep 30, 2026Weifeng YangNonconvex Optimization Constrained Optimization
A QCQP-Representable IMU Pre-Integration Factor for Certifiable State Estimation
Sep 29, 2026Utkarsh Rai, Zhexin Xu, Bang-Shien Chen +1Constrained Optimization Robot State Estimation
Robust Autonomy Lab, Institute for Experiential Robotics, Northeastern University, 360 Huntington Ave, Boston, MA 02115, USA
Learning Samples Importance: Parameterizing Dual Variables in Everywhere Learning
Sep 28, 2026Ignacio Boero, Jonathan Nixon, Alejandro RibeiroConstrained Optimization Sensitivity Analysis
University of Pennsylvania
Learned Preconditioning for a Primal-Dual Interior-Point Method
Sep 28, 2026Abhinav Madabhushi, Jialin Liu, Minxin ZhangPrimal-Dual Optimization Learning to Optimize
Department of Mathematics, University of California, Los Angeles · School of Data, Mathematical, and Statistical Sciences, University of Central Florida
Riemannian Difference-of-Convex Optimization for K-Means Clustering
Sep 28, 2026Meng Xu, Bo Jiang, Hanfu Zhang +2Riemannian Optimization Clustering
AMSS, Chinese Academy of Sciences, and University of Chinese Academy of Sciences, Beijing, China · Ministry of Education Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China · Ministry of Education Key Laboratory of Mathematics and Information Networks, School of Mathematical Sciences, Beijing University of Posts and Telecommunications, Beijing, China +1
dOPT: Differentiating Conic Optimization via Geometric Reduction
Sep 27, 2026Fengyu Yang, Connor W. Magoon, Tyler Watts +1Implicit Differentiation Differentiable Programming
Department of Mathematics University of North Carolina at Chapel Hill
The cost of useful natural gradient updates
Sep 27, 2026Subhransu S. Bhattacharjee, Dylan Campbell, Rahul ShomeSample Complexity Natural Gradient Methods
School of Computing, The Australian National University
Local LMO is Secretly a Projection Method!
Sep 27, 2026Peter Richtárik, Ammar MahranLMO Methods Constrained Optimization
King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
Identifying the Predictable Drift of a Semimartingale from Marginal Laws
Sep 27, 2026Jakub Marecek, Enrico Biffis, Abigail Langbridge +1Latent Dynamics Modeling Constrained Optimization
Department of Computer Science, Czech Technical University in Prague, Czechia · Department of Finance, Imperial College London, UK · Dyson School of Design Engineering, Imperial College London, UK
Decentralized Optimization with Cross-Coupled Mixed Affine Constraints
Sep 26, 2026Ewsey Obzherin, Ilya Khomchenko, Natalia Shelegeda +4Decentralized Optimization Constrained Optimization
Moscow Independent Research Institute of Artificial Intelligence · FusionBrain Lab · Innopolis University
PolyStepOR: Learning to Decide Without Optimal Decisions
Sep 26, 2026Viet The Nguyen, Gunther Gust, An Thai LeDecision-Focused Learning Predict-Then-Optimize
University of Würzburg, Germany · Center for Artificial Intelligence and Data Science (CAIDAS), Germany · Center for AI Research, VinUniversity, Vietnam +1
Game-Theoretic Control with Constrained Potential Surgery
Sep 25, 2026Zhiyuan Zhang, Panagiotis TsiotrasNash Equilibrium Computation Game Theory
School of Aerospace Engineering, Institute for Robotics and Intelligent Machines, Georgia Institute of Technology, Atlanta, GA 30332, USA
LensDesigner: A Self-Improving Agent for Optical Lens Design
Sep 24, 2026Lei Sun, Haoran Liang, Dannong Xu +6Self-Improving Agents Automated Heuristic Design
INSAIT, Sofia University “St. Kliment Ohridski” · Zhejiang University
A Nearly Quadratic Lower Bound for Linear Optimization over Convex Bodies in the Membership Oracle Model
Sep 24, 2026Santosh S. VempalaOracle Complexity Constrained Optimization
Georgia Tech
What, When, and How: Audio Description as Constrained Global Optimization
Sep 24, 2026Igor Sterner, Mirella Lapata, Alex Lascarides +1Audio Description Generation Constrained Optimization
School of Informatics University of Edinburgh United Kingdom
AT-SKM-Net: An Accelerated Trainable Sampling Kaczmarz-Motzkin Framework for Linear Hard-Constraint Feasibility on Dynamic Graphs
Sep 24, 2026Xiaochen Zhang, Haoyu Zhu, Yao Zhang +1Constrained Optimization
Zhejiang University
Amplify: A Lightweight Library for Reproducible Nonlinear Programming Problems in Robotics
Sep 23, 2026Nelson RosaRobotic Optimization Trajectory Optimization
Self-Supervised Combinatorial Optimization with Constraints via Frank-Wolfe
Sep 22, 2026Akbar Rafiey, Yifei Xu, Nikolaos KaraliasSelf-Supervised Learning Combinatorial Optimization
NYU · MIT
Near-Optimal Acceleration for Smooth $\ell_p$ / $\ell_q$ Nondual Convex First-Order Oracle Optimization
Sep 18, 2026David Martínez-Rubio, Brian Bullins, Cristóbal Guzmán +1Accelerated Gradient Methods Constrained Optimization
IMDEA Software Institute, Madrid, Spain · Purdue University, West Lafayette, IN, USA · Institute for Mathematical and Computational Engineering, Faculty of Mathematics and School of Engineering, Pontificia Universidad Cat´olica de Chile, Santiago, Chile +1
Bilevel Optimization of Topology and Hyperparameters (BOTH)
Sep 18, 2026Suryanarayanan Manoj Sanu, Miguel Anibal Bessa, Alejandro Marcos AragónHypergradient Optimization Topology Optimization
Faculty of Mechanical Engineering Delft university of technology Delft The Netherlands · School of engineering Brown University Providence United States of America
Stable Movement for Nondual Lipschitz Convex Optimization: Efficiency and Nearly Optimal Oracle Rates
Sep 17, 2026David Martínez-Rubio, Cristóbal GuzmánConstrained Optimization Nonsmooth Convex Optimization
IMDEA Software Institute, Madrid, Spain · Institute for Mathematical and Computational Engineering, Faculty of Mathematics and School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
DR-MPC: Fast and Feasible Dynamics-Relaxed Model-Predictive Control for Legged Locomotion
Sep 17, 2026Run Wang, Alapati Tuerxun, Shuo Liu +4Model Predictive Control Constrained Optimization
Department of Automation, Tsinghua University, Beijing, China · Department of Mechanical Engineering, Boston University, Brookline, MA, USA · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore +1

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ML-OPF-Bench: Benchmarking Machine Learning for Optimal Power Flow

Xinyi Liu, Xuan He, Danny H. K. Tsang, Yize Chen

Dartmouth College · Hong Kong University of Science and Technology (Guangzhou) · University of Alberta

Optimal Power Flow Learning to Optimize Constrained Optimization

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Machine Learning (ML) methods promise a fast solution process for Optimal Power Flow (OPF). While inconsistent test cases, implementations, and evaluation metrics across existing studies make it challenging to determine which algorithmic advances are most critical for real-world deployment. To this end, we propose ML-OPF-Bench, a unified benchmark for AC- and DC-OPF that evaluates representative ML algorithms under a consistent pipeline, stress-tests them across system sizes, distribution shifts, and resource budgets, and ranks them with a multi-objective framework. We find that prediction accuracy alone is not a reliable indicator of operational feasibility. Under heavily loaded, congested conditions, even the strongest in-distribution performers lose their advantage, while feasibility is maintained largely by post-processing that enforces the target constraints rather than by the underlying pure ML predictor. Data scaling shows that prediction accuracy and constraint violations follow different trajectories, whereas compute scaling shows that returns diminish and that larger models do not consistently perform better. These results expose critical trade-offs among ML methods' speed, accuracy, and feasibility, and offer practical guidance for future ML-OPF design. We open-source the benchmark as an extensible Python package for integrating new learning-based OPF algorithms and evaluating them under the same standard as the existing baselines.