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.

A State-Space Model of Figured-Bass Realization: Local Constraints, Coupled Voices, and Polynomial-Time Solvability
Sep 16, 2026Evan Unit LimSymbolic Music Generation Constrained Optimization
National Taiwan Normal University
ElastiQP: An Always-Feasible QP Solver for Constrained Robot Control
Sep 16, 2026Daniel Morton, Jon Arrizabalaga, Zachary Manchester +1Robotic Control Constrained Optimization
Departments of Mechanical Engineering and Aeronautics & Astronautics, Stanford University, USA · Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, USA
Projection-Free Multi-level Algorithms for Stochastic Constrained Compositional Optimization
Sep 14, 2026Wei Jiang, Sifan Yang, Wenhao Yang +4Stochastic Optimization Nonconvex Stochastic Optimization
School of Computer Science and Engineering, Nanjing University of Science and Technology, China · School of Artificial Intelligence, Nanjing University, China · School of Software Technology, Zhejiang University, China
Generation of Custom Solvers in Rust for Convex Optimization
Sep 12, 2026Hao Zhu, Joschka BoedeckerCode Generation Constrained Optimization
IMBIT//BrainLinks-BrainTools · Department of Computer Science, University of Freiburg
Quality-Constrained Routing over a Fixed Pool of Quantized Mixture-of-Experts Instances
Sep 11, 2026Zhenghong Huang, Hongfan Wu, Jiheng ZhangMixture-of-Experts Inference Mixture-of-Experts Quantization
The Hong Kong University of Science and Technology Clear Water Bay, Kowloon, Hong Kong
Constraint-Aware Discrete Black-Box Optimization Using Tensor Decomposition
Sep 8, 2026Keisuke Onoue, Ryosuke KojimaSurrogate-Assisted Optimization Black-Box Optimization
Nara Institute of Science and Technology, Nara, Japan · Graduate School of Medicine, Kyoto University, Kyoto, Japan · RIKEN Center for Biosystems Dynamics Research, Japan
When Can One Obtain Certificates of Optimality Using Positivstellensaetze?
Sep 8, 2026Nayoon Kim, Allen Gehret, Shenyuan Ma +1Constrained Optimization
Beyond the Matrix Sign: Quadratic Spectral Descent
Sep 7, 2026Qiaozhe Zhang, Jun Sun, Yingzhuang LiuSign-Based Optimization Muon Optimizer
School of Electronic Information and Communications Huazhong University of Science and Technology
Advances in Machine Learning for Directed Evolution: A Five-Year Retrospective
Sep 2, 2026Bruce J. WittmannConstrained Optimization Protein Design
Microsoft, Office of the Chief Scientific Officer
CORAL: An LLM-Native Harness for Production Recommender Systems
Sep 2, 2026Muhammad Rafay Azhar, Yuhang Zhou, Gilbert Jiang +7Recommender Systems LLM Agents
Meta AI
Variable Selection for Feature-Based Newsvendor
Sep 1, 2026Zhaoliang Yuan, Jie WangInventory Control Constrained Optimization
School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen · School of Artificial Intelligence and School of Data Science, The Chinese University of Hong Kong, Shenzhen
Conditional Flow Matching for ML-Based Inverse Design Problems
Sep 1, 2026Juliana Felder, Milad Habibi, Soheyl Massoudi +1Conditional Flow Matching Constrained Optimization
ETH Zürich · University of Maryland, College Park
Disciplined Bilevel Programming
Sep 1, 2026Hao Zhu, Joschka BoedeckerBilevel Optimization Constrained Optimization
IMBIT//BrainLinks-BrainTools · Department of Computer Science, University of Freiburg
Operational Regimes in Non-Convex Optimization: A Multiplier-Based Taxonomy
Aug 31, 2026Seyed Mohsen Kazemi, Ali Movaghar, Shaahin hessabiNonconvex Optimization Constrained Optimization
Department of Computer Engineering, Sharif University of Technology, Azadi, Tehran, 11365-9517, Tehran, Iran.
Denoising as Projection: Constrained Optimization with Gradient-Guided Diffusion
Aug 30, 2026Runyu Zhang, Jiawei Zhang, Gioele Zardini +2Riemannian Optimization Diffusion Guidance
MIT · University of Wisconsin–Madison
CLIPPER: Replayable Shortlisted Optimization for Repeated Spatial Coverage Planning
Aug 27, 2026Julian Teusch, Jörg Philipp Müller, Monika SesterGreedy Optimization Constrained Optimization
Institute of Computer Science, Clausthal University of Technology, Germany · Institute of Cartography and Geoinformatics, Leibniz University Hannover, Germany
CG4AI: A Column Generation Framework for Training AI Models Under Constraints
Aug 26, 2026Youcef Magnouche, Abderrahmane Driouch, Sébastien Martin +1Constrained Optimization
Huawei Technologies Ltd., France Research Center, 18 Quai du Point du Jour, Boulogne-Billancourt, 92100, France.
Parameterized Complexity of $L_p$ -Lipschitz Constants for Input Convex Neural Networks and $L_p$ -Norm Maximization over Zonotopes
Aug 25, 2026Aritra Das, Vincent Froese, Moritz Grillo +6Lipschitz Neural Networks Parameterized Complexity
Ashoka University, Truth Audit Labs · Technische Universität Berlin · Max Planck Institute for Mathematics in the Sciences +3
Constrained Hyperparameter Optimization for Streaming Data
Aug 25, 2026Bruno Veloso, João GamaHyperparameter Optimization Constrained Optimization
FEP - School of Economics and Management, University of Porto, Porto, Portugal · INESC TEC, Porto, Portugal
The Cost of a Physics Prior Is Bounded by the Ablation Gap
Aug 21, 2026Boris KriukMonotonicity Constraints Physics-Informed ML
Department of Computer Science and Engineering, The Hong Kong University of Science and Technology (HKUST), Clear Water Bay, Kowloon, Hong Kong SAR, China
A FEM-Based Surrogate Modelling and Optimization Framework for Physics-Constrained Electromagnetic Coil Design
Aug 19, 2026Yucheng LiuSurrogate-Assisted Optimization Constrained Optimization
Department of Engineering Science University of Oxford Oxford, United Kingdom
Design Optimization for Large High-Force Soft Robot Manipulators Under Gravitational Loads
Aug 17, 2026Isara Cholaseuk, Penelope Llibre, Alexa Kyriacou +5Soft Robotics Constrained Optimization
Department of Mechanical Engineering, Boston University, Boston MA, USA · Division of Systems Engineering, Boston University, Boston MA, USA
CAPO: Constraint-Aware Prompt Optimization for LLM Agents
Aug 17, 2026Victor Ye Dong, Reid Pryzant, Yi Liu +1Prompt Optimization LLM Agent Workflow Optimization
Microsoft · Independent Researcher
Constrained Graph Diffusion for Mixed Integer Optimization
Aug 13, 2026Vincenzo Di Vito, Yusuf Guven, Babak Badnava +3Mixed-Integer Linear Programming Constrained Optimization
University of Virginia · MIT · Los Alamos National Laboratory
ContactIPM: A Structure-Exploiting Interior-Point Solver for Contact-Implicit Trajectory Optimization
Aug 12, 2026Yucheng ChenPrimal-Dual Optimization Trajectory Optimization
Basin: Efficient and Extensible Numerical Optimization in Rust
Aug 11, 2026Johan LarssonConstrained Optimization
Department of Mathematical Sciences, University of Copenhagen, Denmark
Boundary-Seeking Policy Gradient for Safe Reinforcement Learning
Aug 10, 2026Chenhua Fan, Jiahui Zhu, Yuhang Zhang +1Markov Decision Processes Constrained RL
School of EECS, Washington State University, Pullman, WA 99163, USA
From Prediction to Incrementality: Causal Optimization for Large-Scale Targeting and Recommendation
Aug 10, 2026Changshuai Wei, John Bencina, Phuc Nguyen +2Causal Effect Estimation Constrained Optimization
LinkedIn · Seattle, USA · Sunnyvale, USA
DualCert: A Solver for the Traveling Salesman Problem with Constraint-Coupled Learning
Aug 10, 2026Yancheng Song, Yongzhi Qi, Wei Qi +1Traveling Salesperson Problem Primal-Dual Optimization
Department of Industrial Engineering, Tsinghua University, Beijing 100084, China · JD.com, Beijing, China · College of Engineering, UC Berkeley, Berkeley, CA 94720, USA; Faculty of Engineering, Faculty of Business and Economics, University of Hong Kong, Hong Kong, China
Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificates
Aug 8, 2026Rui Wu, Zongyuan Chen, Hong XieScore-Based Causal Discovery Causal Discovery
School of Computer Science and Engineering, University of Science and Technology of China

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A State-Space Model of Figured-Bass Realization: Local Constraints, Coupled Voices, and Polynomial-Time Solvability

Evan Unit Lim

National Taiwan Normal University

Symbolic Music Generation Constrained Optimization Constraint Satisfaction

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Figured-bass realization can be described as a sequence of choices constrained both within each sonority and between successive sonorities. This paper gives an explicit mathematical model of a restricted, examination-style four-part realization problem. Pitch spelling, range, chord membership, doubling, omission, spacing, crossing, overlap, melodic motion, consecutive perfect intervals, and selected resolution requirements are expressed as predicates. We distinguish hard constraints from optional preference costs. Four labeled notes are represented visually as the vertices of a quadrilateral and computationally as one ordered voicing state. Legal progressions become paths through a layered graph. We prove that feasibility and minimum-cost realization are polynomial-time problems for a fixed number of voices with explicit finite note domains and fixed local rules. For fixed ranges, a fixed note alphabet, and adjacent-event rules, the number of graph operations is linear in the number of events. Worked two-, four-, and eight-beat examples illustrate legality, optimization, and the failure of a greedy choice. The result concerns the stated formal model; it is not a claim that every musical judgment is captured by local predicates.