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.

Beyond ESG Scores: Learning Dynamic Constraints for Sequential Portfolio Optimization
May 10, 2026Xin Li, Yan Ke, Longbing CaoConstrained RL Constrained Optimization
Macquarie University · The University of Queensland
IMPACT: An Implicit Active-Set Augmented Lagrangian for Fast Contact-Implicit Trajectory Optimization
May 9, 2026Jiayun Li, Dejian Gong, Georgia ChalvatzakiConstrained Motion Planning Trajectory Optimization
1PEARL Lab, Dept. of Computer Science, TU Darmstadt, Germany · 2Hessian.AI, Darmstadt, Germany · 3Robotics Institute Germany (RIG)
Broximal Gradient Descent: A Projection-Free Sister of Projected Gradient Descent
May 9, 2026Peter Richtárik, Kaja Gruntkowska, Hanmin LiGradient Descent Constrained Optimization
King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
FlowADMM: Plug-and-play ADMM with Flow-based Renoise-Denoise Priors
May 9, 2026Hendrik Sommerhoff, Michael MoellerAlternating Direction Method of Multipliers Image Restoration
Computer Vision Group, University of Siegen Hölderlinstraße 3, 57076 Siegen, Germany
AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Training
May 8, 2026Binghang Lu, Runyu Zhang, Changhong Mou +2Neural PDE Solvers Constrained Optimization
Purdue University · Massachusetts Institute of Technology · Utah State University +1
Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problems
May 8, 2026Yiyang Shen, Yutian He, Weiran Wang +1Min-Max Optimization Bilevel Optimization
University of Iowa
Sensitivity-Based Robust NMPC for Close-Proximity Offshore Wind Turbine Inspection with a Tilted Multirotor
May 8, 2026Giuseppe Silano, Martin SaskaIndustrial Inspection Robust Control
Ricerca sul Sistema Energetico S.p.A., Milan, Italy, and the Czech Technical University in Prague, Czechia · Czech Technical University in Prague, Czechia
SkillSelect-Serve: QoS-Aware Budgeted Skill Service Recommendation for LLM Agents
May 8, 2026Jingyuan Zheng, Dongjing Wang, Xin Zhang +7LLM Agent Skill Retrieval LLM Agents
School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, 310018, China · Sanya Traditional Chinese Medicine Hospital, Sanya, 572000, China · HDU-ITMO Joint Institute, Hangzhou Dianzi University +3
Convex Optimization with Nested Evolving Feasible Sets
May 8, 2026Karthick Krishna M., Haricharan Balasundaram, Rahul VazeOnline Convex Optimization Constrained Optimization
Solving Max-Cut to Global Optimality via Feasibility-Preserving Graph Neural Networks
May 8, 2026Hao Chen, Chendi Qian, Christopher Morris +2Max-Cut Semidefinite Programming
1Davidson School of Chemical Engineering, Purdue University · Faculty of Computer Science, RWTH Aachen University · 3Jacobs Technion-Cornell Institute, Cornell Tech
Matrix-Valued Optimism is Matrix-Valued Augmentation: Additive Hybrid Designs for Constrained Optimization
May 7, 2026Jiayi ZhaoPrimal-Dual Optimization Augmented Lagrangian Method
University of Washington Seattle, WA, USA
WARP: A Benchmark for Primal-Dual Warm-Starting of Interior-Point Solvers
May 7, 2026Dhruv Suri, Helgi Hilmarsson, Shourya BosePrimal-Dual Optimization Graph Neural Networks
Pravah
Convex-Geometric Error Bounds for Positive-Weight Kernel Quadrature
May 7, 2026Satoshi HayakawaConstrained Optimization Kernel Methods
The University of Tokyo
Differentiable Parameter Optimization for DAEs with State-Dependent Events
May 6, 2026Ion Matei, Maksym Zhenirovskyy, Anthony WongDynamical Systems Automatic Differentiation
Fujitsu Research of America
Exact Dual Geometry of SOC-ICNN Value Functions
May 6, 2026Kang Liu, Jianchen Hu, Wei PengSecond-Order Cone Programming Neural Network Optimization
School of Future Technology Xi’an Jiaotong University Xi’an, China · School of Future Technology School of Automation Science and Engineering Xi’an Jiaotong University Xi’an, China · School of Automation Science and Engineering Xi’an Jiaotong University Xi’an, China
Geometry-Aware Neural Optimizer for Shape Optimization and Inversion
May 6, 2026Guoze Sun, Tianya Miao, Haoyang Huang +4Neural Surrogate Modeling Geometric Representation Learning
Gaoling School of Artificial Intelligence, Renmin University of China
Demystifying Manifold Constraints in LLM Pre-training
May 6, 2026Kang An, Jiaxiang Li, Donald Goldfarb +1Language Model Pretraining Riemannian Optimization
Rice University · Independent Researcher · Columbia University
Adaptive Diagonal Loading for Norm Constrained Beamforming
May 5, 2026Manan Mittal, Ryan M. Corey, John R. Buck +1Constrained Optimization
Stony Brook University1 · University of Illinois Chicago2 · University of Massachusetts Dartmouth3
A Provably Convergent and Practical Algorithm for Gromov--Wasserstein Optimal Transport
May 5, 2026Ling Liang, Lei YangGradient Descent Nonconvex Optimization
Department of Mathematics, The University of Tennessee, Knoxville, TN 37916, USA · School of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, Guangdong 510275, China
A second-order method landing on the Stiefel manifold via Newton $\unicode{x2013}$ Schulz iteration
May 4, 2026Xinhui Xiong, Bin Gao, P. -A. AbsilNewton-Schulz Iteration Stiefel Manifold Optimization
State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and University of Chinese Academy of Sciences, China · State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China · ICTEAM Institute, UCLouvain, Belgium
Strategy-Aware Optimization Modeling with Reasoning LLMs
May 4, 2026Ruiqing Zhao, Fengzhi Li, Yuan Zuo +5RL for Code Generation LLM-Based Program Synthesis
School of Computer Science and Engineering, Beihang University, Beijing, China · JIUTIAN Research, Beijing, China · MIIT Key Laboratory of Data and Decision Intelligence, Beihang University, Beijing, China
LUMINA: A Grid Foundation Model for Benchmarking AC Optimal Power Flow Surrogate Learning
May 4, 2026Hongwei Jin, Keunju Song, Zeeshan Memon +5Neural Surrogate Modeling Benchmark Design
Mathematics and Computer Science Division, Argonne National Laboratory · Department of Electronic Engineering, Sogang University · Department of Computer Science, Emory University +1
Optimization of CV-QKD Under Practical Constraints
May 3, 2026Svitlana Matsenko, Amirhossein Ghazisaeidi, Marcin Jarzyna +2Constrained Optimization
DTU Electro, Technical University of Denmark, DK-2800, Kgs. Lyngby, Denmark · Nokia Bell Labs, 91300 Massy, France · Centre for Quantum Optical Technologies, CeNT, University of Warsaw, 02-097 Warszawa, Poland +1
Towards Systematic Generalization for Power Grid Optimization Problems
May 3, 2026Zeeshan Memon, Yijiang Li, Hongwei Jin +2Optimal Power Flow Constrained Optimization
Emory University Atlanta, GA, USA · Argonne National Laboratory Lemont, IL, USA
Augmented Lagrangian Multiplier Network for State-wise Safety in Reinforcement Learning
May 1, 2026Jiaming Zhang, Yujie Yang, Yao Lyu +2Constrained RL Augmented Lagrangian Method
School of Vehicle and Mobility & College of AI, Tsinghua University, Beijing, 100084, China
Model Compression with Exact Budget Constraints via Riemannian Manifolds
May 1, 2026Michael Helcig, Dan AlistarhModel Compression Riemannian Optimization
ETH Zürich · IST Austria
NLPOpt-Net: A Learning Method for Nonlinear Optimization with Feasibility Guarantees
Apr 30, 2026Bimol Nath Roy, Rahul Golder, MM Faruque HasanNeural Network Optimization Learning to Optimize
Texas A&M University
Global Optimality for Constrained Exploration via Penalty Regularization
Apr 30, 2026Florian Wolf, Ilyas Fatkhullin, Niao HeConstrained RL Maximum Entropy RL
The Computing & Mathematical Sciences Department, California Institute of Technology, Pasadena, CA. · Department of Computer Science, ETH Zurich, Switzerland. · 3ETH AI Center, ETH Zurich, Switzerland.
On the Expressive Power of GNNs to Solve Linear SDPs
Apr 30, 2026Chendi Qian, Christopher MorrisSemidefinite Programming Graph Neural Networks
Faculty of Computer Science, RWTH Aachen University, Germany
Learning Over-Relaxation Policies for ADMM with Convergence Guarantees
Apr 29, 2026Junan Lin, Paul J. Goulart, Luca FurieriLearning to Optimize Alternating Direction Method of Multipliers
Department of Engineering Science, University of Oxford, OX1 3PJ Oxford, UK

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Beyond ESG Scores: Learning Dynamic Constraints for Sequential Portfolio Optimization

Xin Li, Yan Ke, Longbing Cao

Macquarie University · The University of Queensland

Constrained RL Constrained Optimization Portfolio Optimization Finance

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ESG-aware portfolio optimization is increasingly important for sustainable capital allocation, yet most learning-based methods still operationalize ESG by appending static scores to the policy observation or reward. This creates a mismatch for sequential control: ESG scores are noisy, provider-dependent, low-frequency, and temporally misaligned with sequential portfolio decisions, while financial evidence suggests that ESG is better treated as a portfolio preference, risk-exposure, or hedge dimension than as a robust alpha factor. We propose to impose ESG constraints without modifying the financial policy's observation or reward, using a Multimodal Action-Conditioned Constraint Field (MACF) that learns mechanism-specific ESG costs from point-in-time multimodal evidence and contemplated portfolio transitions. We then introduce MACF-X, a family of optimizer-specific adapters that converts MACF costs and uncertainties into native constrained-optimization interfaces through a shared slack- and uncertainty-aware pressure layer. Across multiple constraint-integration interfaces, MACF-X reduces tail ESG budget pressure while maintaining competitive financial performance. Ablations show that this improvement depends on dynamic evidence inputs and three-head decomposition, while static ESG-score proxies are nearly indistinguishable from score-shuffled noise baselines.