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.

Neural Slack Variables for Shape Constraints
Jun 11, 2026Ruben Wiedemann, Antoine Jacquier, Lukas GononMonotonicity Constraints Constrained Optimization
Imperial College London London, UK · University of St. Gallen St. Gallen, Switzerland
Different Layers, Different Manifolds: Module-Wise Weight-Space Geometry in Transformer Optimization
Jun 11, 2026Kirato YoshiharaStiefel Manifold Optimization Neural Network Optimization
School of Engineering Science, The University of Osaka, Osaka, Japan.
Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems
Jun 10, 2026Zhen Zhang, Alessandro Alla, George Em KarniadakisConstrained Optimization Physics-Informed ML
Division of Applied Mathematic, Brown University, Providence, RI, USA · Department of Mathematics, Sapienza Università di Roma, Rome, Italy
Range-Aware Bayesian Optimization for Discovering Diverse Designs within Target Property Windows
Jun 10, 2026Shengli Jiang, Jason Wu, Charles M. Schroeder +1Molecular Optimization Bayesian Optimization
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08540, USA
PL-KKT-hPINN: Enforcing Nonlinear Equality Constraints on Neural Networks via Piecewise-Linear Projection
Jun 9, 2026Fateme Mohammad Mohammadi, Hector Budman, Joshua L. PulsipherNeural Surrogate Modeling Constrained Optimization
Department of Chemical Engineering University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada
LieIPM: Lie Group Interior Point Method for Direct Trajectory Optimization of Rigid Bodies
Jun 9, 2026Sangli Teng, Ruiqi Zhang, Tzu-Yuan Lin +5Trajectory Optimization Riemannian Optimization
University of California, Berkeley · MIT · Ohio University +1
Duality for Optimal Multi-Item, Multi-Bidder Auction Design: Revenue Certificates through Deep Learning
Jun 8, 2026Yanchen Jiang, David C. Parkes, Tonghan WangPrimal-Dual Optimization Game Theory
Harvard University, USA · College of AI, Tsinghua University, China
Parameter Tuning with Generalization Guarantees for GPU-Accelerated Linear Programming
Jun 7, 2026Siddharth Prasad, Dravyansh SharmaPrimal-Dual Optimization Constrained Optimization
Toyota Technological Institute at Chicago
Bayesian Optimization of a Multi-Product Chemical Reactor Using Composite Models and Partial Physics Knowledge
Jun 7, 2026Liqiu Dong, Marta Zagórowska, Mehmet MercangözBayesian Optimization Safe Bayesian Optimization
Department of Chemical Engineering, Imperial College London, London, UK · DCSC, Delft University of Technology, Delft, Netherlands
Residual-Controlled Multiplier Learning for Stochastic Constrained Decision-Making
Jun 5, 2026Kang Liu, Jianchen Hu, Ziyu Qu +3Stochastic Optimization Primal-Dual Optimization
School of Future Technology Xi’an Jiaotong University Xi’an, China, 710049 · School of Automation Science and Engineering Xi’an Jiaotong University Xi’an, China, 710049 · School of Mathematics and Physics China University of Geosciences Wuhan, China, 430074 +2
Multi-ResNets for Subspace Preconditioning in Constrained Optimization
Jun 4, 2026Merve Karakas, Christopher J. Williams, Emmanuel O. Balogun +3Residual Learning Learning to Optimize
UCLA · University of Oxford · Sunrun† +1
Finding Most Influential Sets
Jun 4, 2026Lucas D. Konrad, Nikolas KuschnigConstrained Optimization
Vienna University of Economics and Business, Austria · Monash University, Australia
R-APS: Compositional Reasoning and In-Context Meta-Learning for Constrained Design via Reflective Adversarial Pareto Search
Jun 3, 2026João Pedro Gandarela, Thiago Rios, Stefan Menzel +1Mechanism Design Meta-Learning
Idiap Research Institute, Switzerland · École Polytechnique Fédérale de Lausanne (EPFL), Switzerland · Honda Research Institute Europe, Germany +2
DiffSlack: Learning under Nonlinear Inequality Constraints via Learnable Slack Variables
Jun 3, 2026Ziqian Wang, Chenxi Fang, Zhen ZhangConstrained Optimization Differentiable Optimization
State Key Laboratory of Tribology in Advanced Equipment, Tsinghua University, Beijing 100084, China · Beijing Key Laboratory of Transformative High-end Manufacturing Equipment and Technology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China · Automotive Electronics Business Unit at Hirain Inc., China
Optuna Constrained Tree-Structured Parzen Estimator Is a Joint Density Generalization of c-TPE
Jun 3, 2026Shuhei Watanabe, Kaichi IrieBayesian Optimization Constrained Optimization
Independent Researcher · Kyoto University
Rethinking Neural Width for Alternating Current Optimal Power Flow Proxies
Jun 2, 2026Dhruvi Khandelwal, Anurag Basistha, Ayushi Jolotia +1Neural Surrogate Modeling Optimal Power Flow
Department of Electrical Engineering, National Institute of Technology Kurukshetra, India. · Indraprastha Institute of Information Technology Delhi, India. · Department of Electrical Engineering, Indian Institute of Technology Roorkee, India.
The Shadow Price of Reasoning: Economic Perspective on Optimal Budget Allocation for LLMs
Jun 2, 2026Xu Wan, Speed Zhu, Jianwei Cai +4Cost-Aware Inference Inference-Time Scaling
1Zhejiang University · 2Tecent HY Team · 3Peking University
Coordination Graphs for Constrained Multi-Agent Reinforcement Learning
Jun 1, 2026Santiago Amaya-Corredor, Miguel Calvo-Fullana, Anders JonssonMulti-Objective Reinforcement Learning Multi-Agent System Optimization
Department of Engineering, Universitat Pompeu Fabra, Barcelona, Spain
Everywhere Learning: Artificial Intelligence with Pointwise Constraints
Jun 1, 2026Ignacio Boero, Ignacio Hounie, Luiz Chamon +1Constrained Optimization Statistical Learning Theory
Department of Electrical and Systems Engineering, University of Pennsylvania · École polytechnique, Institut Polytechnique de Paris
Global Convergence of a Line-Search Filter Differential Dynamic Programming Method
May 31, 2026Ming Xu, Iman ShamesOptimization Convergence Analysis Constrained Optimization
School of Computer and Communication Sciences EPFL 1015 Lasanne, Switzerland · Department of Electrical and Electronic Engineering University of Melbourne Parkville, VIC, 3010, Australia
Infeasible optimization problems and the hierarchical augmented Lagrangian method in imitation learning
May 30, 2026Roland Andrews, Justin Carpentier, Ajay SathyaImitation Learning Augmented Lagrangian Method
Unlearning in Diffusion Models: A Unified Framework with KL Divergence and Likelihood Constraints
May 29, 2026Shervin Khalafi, Alejandro Ribeiro, Dongsheng DingPrimal-Dual Optimization Diffusion Model Unlearning
University of Pennsylvania · University of Tennessee, Knoxville
Exploiting Chordal Sparsity for Globally Optimal Estimation with Factor Graphs
May 28, 2026Avinash Subramanian, Connor Holmes, Timothy D. Barfoot +2Semidefinite Programming Factor Graph Optimization
College of Computing, Georgia Institute of Technology, Atlanta, GA, USA · Robotics Institute, University of Toronto, Toronto, ON, Canada · Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA
Bound-Constrained Sparse Representation for Electrical Impedance Tomography
May 27, 2026Chun Zhang, Dong LiuSparse Recovery Image Reconstruction
School of Biomedical Engineering and Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou 215123, China · Laboratory of Spin Magnetic Resonance and Anhui Province Key Laboratory of Scientific Instrument Development and Application, University of Science and Technology of China, Hefei 230026, China · Jiangsu Provincial Key Laboratory of Multimodal Digital Twin Technology, Suzhou 215123, China
Constrained Auto-Bidding via Generative Response Modeling
May 27, 2026Eunseok Yang, Xingdong Zuo, Kyung-Min KimAutomated Bidding Online Advertising
NAVER Corporation Seongnam-si, Republic of Korea
Developing a Totally Unimodular Linear Program for Optimal Conformance Checking: When and Why It Complements A*
May 26, 2026Izack CohenAlgorithm Selection Process Mining
aFaculty of Engineering, Bar-Ilan University, Ramat Gan, Israel
Blocked Gibbs meets Diffusion Transformers: Unsupervised Learning for Constraint Optimization
May 24, 2026Yudong W. Xu, Wenhao Li, Xiaoyu Wang +2Diffusion Transformer Constrained Optimization
University of Toronto · Vector Institute
Mitigating Gradient Pathology in PINNs through Aligned Constraint
May 24, 2026Yichen Luo, Peiyu Zhu, Dongxiao Hu +5Neural PDE Solvers Gradient Interference
Department of Information Science and Engineering, KTH Royal Institute of Technology, Stockholm, Sweden · School of Advanced Manufacturing and Robotics, Peking University, Beijing, China · School of Advanced Technology, Xi’an Jiaotong-Liverpool University, Suzhou, China +2
Manifold-Constrained MPPI: Real-Time Sampling-Based Control for Nonlinear Equality-Constrained Robotic Systems
May 24, 2026Seulchan Lee, Sanghyun KimRobotic Control Constrained Motion Planning
School of Mechanical Engineering, Kyung Hee University, Yongin, South Korea
Scalable Heterogeneous Graph Foundation Models for Data-Driven Optimal Power Flow in Smart Grids
May 22, 2026Massimiliano Lupo Pasini, Yijiang Li, Kibaek Kim +1Neural Surrogate Modeling Heterogeneous GNNs
Computational Sciences and Engineering Division, Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37831, USA

Jun 11, 2026J/K move · Enter open · S save

Neural Slack Variables for Shape Constraints

Ruben Wiedemann, Antoine Jacquier, Lukas Gonon

Imperial College London London, UK · University of St. Gallen St. Gallen, Switzerland

Monotonicity Constraints Constrained Optimization

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Enforcing functional inequality constraints such as monotonicity and convexity in neural networks is a fundamental challenge in many industrial and scientific applications. Classical one-sided penalty methods, along with primal-dual methods gated by complementary slackness, provide constraint gradients only at violated locations, resulting in fragile satisfaction. Architectures that guarantee feasibility by construction, on the other hand, remain largely limited to elementary cases and impose additional inductive biases. We introduce neural slack variables, a deep learning native primal-side approach that converts constraint enforcement into a regression problem by coupling the primary network with a jointly learned auxiliary network. The auxiliary network serves as a valid target for the primary network's constraint quantities, inducing feasibility and regularity. Neural slack variables achieve zero measured violations on dense-grid monotonicity and convexity test cases, where penalty and primal-dual baselines leave residual violations, and enable arbitrage-free learning of volatility surfaces, an open industrial challenge in quantitative finance.