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

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

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
From Sequential Nodes to GPU Batches: Parallel Branch and Bound for Optimal $k$ -Sparse GLMs
May 21, 2026Jiachang Liu, Andrea LodiBranch and Bound GPU Kernel Optimization
∗Center for Data Science for Enterprise and Society, Cornell University, Ithaca, USA · †School of Operations Research and Information Engineering, Cornell University, Ithaca, USA · ‡Jacobs Technion-Cornell Institute, Cornell Tech and Technion–IIT, New York, USA
CMC-Opt: Constraint Manifold with Corners for Inequality-Constrained Optimization
May 20, 2026Yetong Zhang, Frank DellaertKinodynamic Motion Planning Riemannian Optimization
College of Computing Georgia Institute of Technology Atlanta, USA
Time-Dependent PDE-Constrained Optimization via Weak-Form Latent Dynamics
May 20, 2026April Tran, Terry Haut, David Bortz +1Latent Dynamics Modeling PDE Surrogate Modeling
Department of Applied Mathematics, University of Colorado, Boulder, CO, 80309, USA · Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, 94550, CA, USA
Exploiting Non-Negativity in DAG Structure Learning
May 19, 2026Samuel Rey, Madeline navarro, Santiago Segarra +1Graph Structure Learning Structural Causal Models
Dept. of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA
From SGD to Muon: Adaptive Optimization via Schatten-p Norms
May 19, 2026Thomas Massena, Corentin Friedrich, Mathieu SerrurierLMO Methods Neural Network Optimization
DTIPG - SNCF, IRIT · IRIT
An Exterior Method for Nonnegative Matrix Factorization
May 19, 2026Qiujing Lu, Tonmoy Monsoor, Ehsan Ebrahimzadeh +2Non-Negative Matrix Factorization Low-Rank Matrix Decomposition
1ECE, UCLA · 2eBay Search Science Team
Provably Data-driven Lagrangian Relaxation for Mixed Integer Linear Programming
May 18, 2026Tung Quoc Le, Anh Tuan Nguyen, Viet Anh NguyenMixed-Integer Linear Programming Learning to Optimize
Université Grenoble Alpes, LJK, CNRS, Grenoble INP, 38000 Grenoble, France · Carnegie Mellon University, Machine Learning Department · Chinese University of Hong Kong, Department of Systems Engineering and Engineering Management.
Stochastic Penalty-Barrier Method for Constrained Machine Learning
May 18, 2026Adam Bosák, Andrii Kliachkin, Gilles Bareilles +4Constrained Optimization
Artificial Intelligence Center, CTU in Prague · CMAP, École Polytechnique, Palaiseau, France
New Insight of Variance reduce in Zero-Order Hard-Thresholding: Mitigating Gradient Error and Expansivity Contradictions
May 18, 2026Xinzhe Yuan, William de Vazelhes, Bin Gu +1Zeroth-Order Optimization Constrained Optimization
Harbin Institute of Technology · IASM, Harbin Institute of Technology · Mohamed bin Zayed University of Artificial Intelligence +2
Adaptive Stochastic Natural Gradient Method for Safe Optimization on Binary Space
May 18, 2026Kento Uchida, Ryoki Hamano, Masahiro Nomura +1Black-Box Optimization Natural Gradient Methods
Yokohama National University Yokohama, Kanagawa, Japan · CyberAgent Shibuya, Tokyo, Japan · Institute of Science Tokyo Meguro, Tokyo, Japan
Stochastic Compositional Optimization via Hybrid Momentum Frank--Wolfe
May 14, 2026El Mahdi Chayti, Mohamad FakhouriStochastic Optimization Momentum Methods
Machine Learning and Optimization Laboratory (MLO) EPFL, Switzerland
TinySDP: Real Time Semidefinite Optimization for Certifiable and Agile Edge Robotics
May 13, 2026Ishaan Mahajan, Jon Arrizabalaga, Andrea Grillo +4Semidefinite Programming Constrained Motion Planning
Columbia University, USA · Massachusetts Institute of Technology, USA · ´Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Switzerland +1
Optimal Policy Learning under Budget and Coverage Constraints
May 12, 2026Giovanni CerulliPolicy Optimization Combinatorial Optimization
CNR-IRCrES · National Research Council of Italy · Research Institute on Sustainable Economic Growth
Large Language Models as Amortized Pareto-Front Generators for Constrained Bi-Objective Convex Optimization
May 12, 2026Peipei Xu, SiYuan Ma, Yaohua Liu +4Large Language Model-Guided Optimization Constrained Optimization
University of Shanghai for Science and Technology · The Hong Kong University of Science and Technology
Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives
May 12, 2026Konstantinos Oikonomidis, Jan Quan, Kimon Antonakopoulos +3Nonconvex Stochastic Optimization Muon Optimizer
KU Leuven, Department of Electrical Engineering, STADIUS Center for Dynamical Systems, Signal Processing, and Data Analytics · ´Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Laboratory for Information and Inference Systems (LIONS) · CVN, CentraleSup´elec, Universit´e Paris-Saclay, Inria
GAR: Carbon-Aware Routing for LLM Inference via Constrained Optimization
May 12, 2026Disha Sheshanarayana, Rajat Subhra Pal, Manjira Sinha +1LLM Inference Efficiency Constrained Optimization
Manipal University Jaipur · TCS Research
Primal-Dual Policy Optimization for Linear CMDPs with Adversarial Losses
May 12, 2026Kihyun Yu, Seoungbin Bae, Dabeen LeePrimal-Dual Optimization Markov Decision Processes
Department of Industrial and Systems Engineering KAIST · Department of Mathematical Sciences Seoul National University · Research Institute of Mathematics, Seoul National University; Interdisciplinary Program in Artificial Intelligence, Seoul National University; Korea Institute for Advanced Study
Efficient and provably convergent end-to-end training of deep neural networks with linear constraints
May 12, 2026Zonglin Yang, Zhexuan Gu, Yancheng YuanDeep Learning Optimization Backpropagation
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong
ADMM-Q: An Improved Hessian-based Weight Quantizer for Post-Training Quantization of Large Language Models
May 11, 2026Ryan Lucas, Mehdi Makni, Xiang Meng +2LLM Quantization Alternating Direction Method of Multipliers
MIT Operations Research Center · MIT Sloan School of Management · MIT Center for Statistics
Exact Fixed-Point Constraints in Neural-ODEs with Provable Universality
May 11, 2026Feliciano Giuseppe Pacifico, Duccio Fanelli, Lorenzo Buffoni +3Constrained Optimization Neural Network Approximation Theory
Department of Informatics and Computer Science, University of Pisa, Italy · Department of Physics and Astronomy and INFN, University of Florence, Sesto Fiorentino, Italy
Meta-Black-Box Optimization Can Do Search Guidance for Expensive Constrained Multi-Objective Optimization
May 11, 2026Yukun Du, Haiyue Yu, Jiang Jiang +5Constrained Optimization Multi-Objective Optimization
National University of Defense Technology, Changsha, Hunan, China.
From Single-Step Edit Response to Multi-Step Molecular Optimization
May 11, 2026Haojie Rao, Kun Li, Yida Xiong +5Molecular Optimization Constrained Optimization
School of Computer Science, Wuhan University, Wuhan, China · School of Computer Science, Wuhan University Wuhan, China · Department of Data Science and Artificial Intelligence, Monash University, Victoria, Australia +5
Selection of the Best Policy under Fairness Constraints for Subpopulations
May 11, 2026Tingyu Zhu, Yuhang Wu, Zeyu ZhengMulti-Armed Bandits Group Fairness
Department of Industrial Engineering and Operations Research & Berkeley Artificial Intelligence Research Lab University of California Berkeley
Primal-Dual Guided Decoding for Constrained Discrete Diffusion
May 10, 2026Federico Tomasi, Dmitrii Moor, Alice Wang +1Primal-Dual Optimization Constrained Generative Modeling
Spotify
RDEx-CASK: Cauchy Mutation, Archive, and Stagnation Kick for RDEx-CSOP
May 10, 2026Dikshant, Dikshit Chauhan, Chen Hao +3Differential Evolution Evolutionary Optimization
Learning to Bid with Unknown Private Values in Budget-Constrained First-Price Auctions
May 10, 2026Zihao Hu, Yuxiao Wen, Yuan Yao +2Primal-Dual Optimization Constrained Optimization
Department of Mathematics, The Hong Kong University of Science and Technology · Department of IEDA, The Hong Kong University of Science and Technology · Stern School of Business, New York University
Mismatch-Aware Adaptive Constraint Tightening for Bicycle-Model Trajectory Optimization
May 10, 2026Lingxue Lyu, Zihui LiuTrajectory Optimization Model Predictive Control
School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104, USA · Department of Aeronautics & Astronautics, Stanford University, Stanford, CA 94305, USA
Mutual Information Optimal Density Control of Linear Systems and Generalized Schrödinger Bridges with Reference Refinement
May 10, 2026Shoju Enami, Kenji KashimaStochastic Optimal Control Schrödinger Bridges
Graduate School of Informatics, Kyoto University, Kyoto, Japan

May 24, 2026J/K move · Enter open · S save

Manifold-Constrained MPPI: Real-Time Sampling-Based Control for Nonlinear Equality-Constrained Robotic Systems

Seulchan Lee, Sanghyun Kim

School of Mechanical Engineering, Kyung Hee University, Yongin, South Korea

Robotic Control Constrained Motion Planning Constrained Optimization MPPI Control

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Sampling-based model predictive control methods, such as Model Predictive Path Integral (MPPI), offer derivative-free optimization and robustness in complex robotic systems. However, standard MPPI relies on cost-based soft penalties that cannot guarantee hard-constraint satisfaction, severely limiting its applicability to highly constrained tasks such as closed-chain manipulation. To address this, we propose Manifold-Constrained MPPI (MC-MPPI), a real-time sampling-based control framework that regulates nonlinear equality constraints while preserving the computational advantages of MPPI. The key idea is to decouple the constrained optimal control problem into latent-space planning and execution-level correction. At the planning stage, a Variational Autoencoder (VAE) learns a low-dimensional latent representation of the constraint manifold, enabling MPPI to efficiently generate near-feasible candidate trajectories without per-sample modification. Since this reference enables accurate linearization of the equality constraints, an execution-level Quadratic Programming (QP) controller resolves the residual manifold mismatch in a single solve rather than through iterative projection. Experiments on a 14-DoF closed-chain dual-arm system in both simulation and real-world settings demonstrate 100 Hz planning and 500 Hz execution, equality-residual regulation in static and dynamic environments, and a 95% success rate over 40 randomized hardware trials. Supplementary videos and implementation details are available at https://rcilab.github.io/mcmppi.