Nonconvex Optimization

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Exploiting Non-Negativity in DAG Structure Learning
May 19, 2026Samuel Rey, Madeline navarro, Gonzalo MateosGraph Structure Learning Structural Causal Models
Dept. of Signal Theory and Communications, Universidad Rey Juan Carlos, Madrid, Spain · Dept. of Electrical and Computer Engineering, Rice University, Houston, TX 77005, USA · Dept. of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA
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
Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization
May 18, 2026Yury Demidovich, Abhishek Chakraborty, Grigory Malinovsky +2Muon Optimizer Nonconvex Optimization
King Abdullah University of Science and Technology · Arizona State University
Proximal basin hopping: global optimization with guarantees
May 18, 2026Guillaume Lauga, Cesare Molinari, Samuel VaiterGlobal Optimization Nonconvex Optimization
LJAD · LJAD Université Côte d’Azur France · MaLGA +3
Global Convergence of Sampling-Based Nonconvex Optimization through Diffusion-Style Smoothing
May 15, 2026Zeji Yi, Chaoyi Pan, Guanya Shi +1Optimization Convergence Analysis Black-Box Optimization
Carnegie Mellon University
Min-Max Optimization Requires Exponentially Many Queries
May 13, 2026Martino Bernasconi, Matteo Castiglioni, Andrea Celli +1Query Complexity Oracle Complexity
Bocconi University · Politecnico di Milano · University of Oxford
Parameterized Complexity of Stationarity Testing for Piecewise-Affine Functions and Shallow CNN Losses
May 11, 2026Yuhan YeShallow Neural Networks Nonconvex Optimization
MIT
Fix the Loss, Not the Radius: Rethinking the Adversarial Perturbation of Sharpness-Aware Minimization
May 11, 2026Jinping Wang, Qinhan Liu, Zhiwu Xie +1Neural Network Generalization Sharpness-Aware Minimization
Wenzhou-Kean University · International Frontier Interdisciplinary Research Institute, Wenzhou-Kean University
Dimension-Free Saddle-Point Escape in Muon
May 10, 2026Yanlin Long, Yufei Gu, Zeke XieMuon Optimizer Nonconvex Optimization
xLeaF Lab, The Hong Kong University of Science and Technology (Guangzhou)
Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets
May 9, 2026Saeed Masiha, Zebang Shen, Negar Kiyavash +1Nonconvex Optimization Bilevel Optimization
EPFL School of Management of Technology, Station 5, 1015 Lausanne, Switzerland · ETH Department of Computer Science, Universitätstrasse 6, 8092 Zürich, Switzerland
FedVSSAM: Mitigating Flatness Incompatibility in Sharpness-Aware Federated Learning
May 9, 2026Bingnan Xiao, Yuan Gao, Bingcong Li +3Sharpness-Aware Minimization Non-IID Federated Learning
Fudan University · ETH Zurich · Edith Cowan University +1
Exploring the non-convexity in machine learning using quantum-inspired optimization
May 8, 2026Kandula Eswara Sai Kumar, Parth Dhananjay Danve, Abhishek Chopra +1Evolutionary Optimization Quantum-Inspired ML
1*BosonQ Psi (BQP), New York, USA.
Flatness and Gradient Alignment Are Both Necessary: Spectral-Aware Gradient-Aligned Exploration for Multi-Distribution Learning
May 8, 2026Aristotelis Ballas, Christos DiouSharpness-Aware Minimization Multi-Task Learning
Department of Informatics and Telematics Harokopio University of Athens Omirou 9, Athens, Greece
Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions
May 7, 2026Haitham Kanj, Kiryung LeeGradient Descent Sample Complexity
Department of Electrical and Computer Engineering The Ohio State University, Columbus, OH, USA
When Descent Is Too Stable: Event-Triggered Hamiltonian Learning to Optimize
May 7, 2026Yi Wang, Chandrajit BajajDynamical Systems Learning to Optimize
1Oden Institute · Department of Computer Science
Convexity in Disguise: A Theoretical Framework for Nonconvex Low-Rank Matrix Estimation
May 6, 2026Chengyu Cui, Gongjun XuNonconvex Optimization
Department of Statistics, University of Michigan
Graph Normalization: Fast Binarizing Dynamics for Differentiable MWIS
May 6, 2026Laurent GuiguesDynamical Systems Replicator Dynamics
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 Parameter-Free First-Order Algorithm for Non-Convex Optimization with $\tilde{\mkern1mu O}(ε^{-5/3})$ Global Rate
May 4, 2026Sichao Xiong, Sadok Jerad, Coralia CartisOptimization Convergence Analysis Gradient Descent
Department of Computer Science University of Oxford Oxford, OX1 3QG · Mathematical Institue University of Oxford Oxford, OX2 6GG
A Layer Separation Optimization Framework for Cross-Entropy Training in Deep Learning
Apr 25, 2026Yaru Liu, Michael K. Ng, Yiqi GuDeep Learning Optimization Nonconvex Optimization
School of Mathematical Sciences, University of Electronic Science and Technology of China, Sichuan 611731, China · Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
A Unified Fractional Regularization Framework for Sparse Recovery
Apr 25, 2026Yinhao Zhao, Haoyu He, Chuanqi Ma +1Sparse Recovery Nonconvex Optimization
School of Information Science and Technology, ShanghaiTech University, 201210
An Efficient Multilevel Preconditioned Nonlinear Conjugate Gradient Method for Incremental Potential Contact
Apr 21, 2026Yu Zhang, Xing Shen, Kemeng Huang +5Nonconvex Optimization
S-Lab, Nanyang Technological University, Singapore · Shanghai AI Laboratory, China · University of Hong Kong, China +3
Towards Fully Parameter-Free Stochastic Optimization: Grid Search with Self-Bounding Analysis
Apr 18, 2026Yuheng Zhao, Yu-Hu Yan, Amit Attia +3Stochastic Optimization Nonconvex Stochastic Optimization
National Key Laboratory for Novel Software Technology, Nanjing University, China · School of Artificial Intelligence, Nanjing University, China · Tel Aviv University
ADMM-based Continuous Trajectory Optimization in Graphs of Convex Sets
Mar 11, 2026Lukas Pries, Jon Arrizabalaga, Zachary Manchester +1Trajectory Optimization Alternating Direction Method of Multipliers
Autonomous Aerial Systems Lab, Dep. of Aerospace and Geodesy, TU Munich, Germany · Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, USA
BalLOT: Balanced $k$ -means clustering with optimal transport
Dec 5, 2025Wenyan Luo, Dustin G. MixonClustering Nonconvex Optimization
Department of Mathematics, The Ohio State University, Columbus, Ohio, USA · Translational Data Analytics Institute, The Ohio State University, Columbus, Ohio, USA
On the Condition Number Dependency in Bilevel Optimization
Nov 27, 2025Lesi Chen, Jingzhao ZhangNonconvex Optimization Bilevel Optimization
IIIS, Tsinghua University
Anytime-Feasible First-Order Optimization via Safe Sequential QCQP
Nov 24, 2025Jiarui Wang, Mahyar FazlyabConstrained Optimization Nonconvex Optimization
Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD 21218 USA
Power Homotopy for Zeroth-Order Non-Convex Optimizations
Nov 17, 2025Chen XuZeroth-Order Optimization Nonconvex Optimization
Department of Engineering, Shenzhen MSU-BIT University, China.
Disciplined Biconvex Programming
Nov 3, 2025Hao Zhu, Joschka BoedeckerNonconvex Optimization Constrained Optimization
IMBIT//BrainLinks-BrainTools · Department of Computer Science, University of Freiburg
The Optimization Landscape of Carathéodory Decomposition of Toeplitz Covariances
Nov 3, 2025Daniel Busbib, Ami WieselNonconvex Optimization Matrix Optimization
School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
Smooth Quasar-Convex Optimization with Constraints
Oct 2, 2025David Martínez-RubioRiemannian Optimization Nonconvex Optimization
IMDEA Software Institute · Madrid, Spain
Convergence Analysis of the ProbAbilistic Gradient Estimator Algorithm for Weakly Convex Finite-Sum Optimization
Aug 31, 2025Laurent Condat, Peter RichtárikStochastic Optimization Nonconvex Stochastic Optimization
King Abdullah University of Science and Technology (KAUST) Thuwal, Kingdom of Saudi Arabia
Douglas-Rachford Splitting for Group-Sparse Feedback Linear-Quadratic Control
Jul 26, 2025Lechen Feng, Xun Li, Yuan-Hua NiDistributed Optimization Nonconvex Optimization
Department of Applied Mathematics, The Hong Kong Polytechnic University, China · College of Artificial Intelligence, Nankai University, Tianjin, China
Quantum Speedups for Sampling and Non-convex Optimization with Stochastic Oracles
Apr 4, 2025Guneykan Ozgul, Xiantao Li, Mehrdad Mahdavi +1Markov Chain Monte Carlo Stochastic Gradient Langevin Dynamics
Department of Computer Science and Engineering, Pennsylvania State University, University Park, PA, USA · Department of Mathematics, Pennsylvania State University, University Park, PA, USA
Convergence of Sharpness-Aware Minimization Algorithms using Increasing Batch Size and Decaying Learning Rate
Sep 16, 2024Hinata Harada, Hideaki IidukaSharpness-Aware Minimization Nonconvex Optimization
Department of Computer Science Meiji University
Accelerated Stochastic Min-Max Optimization Based on Bias-corrected Momentum
Jun 18, 2024Haoyuan Cai, Sulaiman A. Alghunaim, Ali H. SayedMomentum Methods Nonconvex Stochastic Optimization
Ecole Polytechnique Fédérale de Lausanne, Switzerland · Kuwait University, Kuwait

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Exploiting Non-Negativity in DAG Structure Learning

Samuel Rey, Madeline navarro, Gonzalo Mateos

Dept. of Signal Theory and Communications, Universidad Rey Juan Carlos, Madrid, Spain · Dept. of Electrical and Computer Engineering, Rice University, Houston, TX 77005, USA · Dept. of Electrical and Computer Engineering, University of Rochester, Rochester, NY 14627, USA

Graph Structure Learning Structural Causal Models Causal Structure Learning Nonconvex Optimization Augmented Lagrangian Method Constrained Optimization

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This work addresses the problem of learning directed acyclic graphs (DAGs) from nodal observations generated by a linear structural equation model. DAG learning is a central task in signal processing, machine learning, and causal inference, but it remains challenging because acyclicity is a global combinatorial property. Continuous acyclicity constraints have led to important algorithmic advances by replacing the discrete DAG constraint with smooth equality constraints. However, existing formulations still involve difficult non-convex optimization landscapes and may suffer from degenerate first-order optimality conditions. Here, we restrict attention to DAGs with non-negative edge weights and exploit this additional structure to obtain a simpler characterization of acyclicity. Building on this characterization, we formulate a regularized non-negative DAG learning problem and develop an algorithm based on the method of multipliers. We further analyze the benign optimization landscape induced by non-negativity. In the population regime, we show that the true DAG is the unique global minimizer of the proposed augmented-Lagrangian formulation; moreover, the landscape contains no spurious interior stationary points, and the true DAG is the only acyclic KKT point. Numerical experiments on synthetic and real-world data show that the proposed method improves over state-of-the-art continuous DAG-learning alternatives.

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