Nonconvex Optimization

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Overview

Nonconvex optimization studies how to find useful solutions when objectives may have many local minima, saddle points, or irregular regions, as in deep learning, matrix recovery, control, and clustering. Common approaches include gradient and stochastic-gradient methods, proximal and difference-of-convex algorithms, alternating and coordinate updates, and manifold-aware methods; global search and convex relaxations are used when stronger guarantees are needed. Theory often measures progress through stationarity and analyzes convergence rates under assumptions such as smoothness, weak convexity, or gradient domination, while benchmarks test performance on large-scale and application-specific problems. A central tension is that efficient methods can often guarantee a stationary point, but proving global optimality or escaping poor solutions may require stronger assumptions, more computation, or problem-specific structure.

Latest papers

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147 papers21 papers in the last four weeks, up 31% on the four weeks before. 0.1% of all new papers.

  1. A knowledge-driven nonconvex square-root regularization framework for joint group sparsity and structured smoothness

    Oct 26, 2026Wanling Xie, Hu YangStructured SparsitySparse Recovery

    College of Mathematics and Statistics, Hunan University of Technology and Business, Changsha, Hunan 410205, China · College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

  2. A Nonconvex Framework for Joint Sparse Sample Weighting and Parameter Estimation

    Oct 25, 2026Hassan Nojavan, Chul Moon, Miju AhnInstance ReweightingRobust Estimation

    Department of Operations Research and Engineering Management, Southern Methodist University · Department of Statistics and Data Science, Southern Methodist University

  3. Decentralized Bi-Level Optimization for Cooperative Orbital Transportation of a Rigid Payload

    Oct 22, 2026Sidhdharth D. Sikka, Revathy Ravuri, Hei Yin Jowett Chan +2Trajectory OptimizationMulti-Robot Cargo Transportation

    Purdue University, West Lafayette, IN 47907 USA · Manifold Research Group, San Francisco, CA 94110 USA · University of Manchester, Manchester M13 9PL, United Kingdom

  4. Curvature-Scaled Sharpness-Aware Minimization: Convergence Beyond Smoothness

    Oct 21, 2026Dimitris Oikonomou, Nicolas LoizouSharpness-Aware MinimizationOptimization Convergence Analysis

    Mathematical Institute for Data Science (MINDS), Johns Hopkins University · Department of Computer Science, Johns Hopkins University · Department of Applied Mathematics and Statistics, Johns Hopkins University

  5. Lower Bounds for Smooth Nonconvex Zeroth-Order Optimization: The Price of Determinism under Low Curvature Trace

    Oct 20, 2026Yuxing Peng, Zhiqing Tang, Weijia JiaZeroth-Order OptimizationNonconvex Optimization

    Faculty of Arts and Sciences, Beijing Normal University, Zhuhai 519087, China · Institute of Artificial Intelligence and Future Networks, Faculty of Arts and Sciences, Beijing Normal University, Zhuhai 519087, China · Guangdong Key Lab of AI and Multi-Modal Data Processing, Beijing Normal-Hong Kong Baptist University, Zhuhai 519087, China

  6. How Finite-Rank Bottlenecks Shape the Low-Rank Adaptation Landscape

    Oct 16, 2026Long Nguyen-Chi, Quynh Nguyen, Thanh Nguyen-Cung +1Low-Rank AdaptationNonconvex Optimization

    College of Engineering & Computer Science, VinUniversity · Center for AI Research, VinUniversity, Hanoi, Vietnam.

  7. Generalization Guarantees of Randomized Block Coordinate Descent for Nonconvex Learning

    Oct 15, 2026Ruixi Hu, Liang WuAlgorithmic GeneralizationGeneralization Bounds

    Center of Statistical Research, School of Statistics and Data Science, Southwestern University of Finance and Economics, Chengdu, China

  8. On the Optimisation Landscape of Overparameterised Weighted MMD

    Oct 14, 2026Tharrshann Jayan Logarajah, Jeremias Knoblauch, Louis SharrockOverparameterizationMaximum Mean Discrepancy

    University College London

  9. Graph Coarsening Enables Escaping Local Optima in Compute-Constrained Nonconvex MAX-CUT

    Oct 13, 2026M. Harper Langston, Pierre-David Letourneau, Dalton Jones +7Max-CutCombinatorial Optimization

    Qualcomm AI Research

  10. Learning to Design Convex Relaxations for Nonconvex Optimization

    Oct 12, 2026Jinrun Liu, Bai Yan, Tengfei Liu +5Convex RelaxationNonconvex Optimization

    Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China · School of Computer Science and Technology, Dongguan University of Technology, Dongguan 523808, China · School of Artificial Intelligence and Computer Science, Shaanxi Normal University, Xi’an 710119, China

  11. From Parallel to Sequential: Small-Batch Noise Restores Simplicity Bias of Muon

    Oct 12, 2026Tom Jacobs, Rebekka BurkholzMuon OptimizerNonconvex Optimization

    CISPA Helmholtz Center for Information Security, Germany

  12. Calibrated αα-Barycenters for Multiobjective ff-Divergence Optimization

    Oct 12, 2026Dier Tang, Peijie Li, Xiaoyuan ZhangMulti-Objective OptimizationSecond-Order Optimization

    The University of Hong Kong · Zhongguancun Academy

  13. Taming Nonconvexity with Epigraph Lifting

    Oct 12, 2026Clara Lage, Hok Shing Wong, Matthias EhrhardtNonconvex OptimizationInverse Problems

    Institut Camille Jordan, École Centrale de Lyon · LMU Munich, Munich Center for Machine Learning · University of Bath

  14. Composite Online-to-Nonconvex Conversion with Optimal Oracle Complexity

    Oct 8, 2026Mingyi Li, Taira Tsuchiya, Kenji YamanishiNonconvex Stochastic OptimizationNonconvex Optimization

    The University of Tokyo · The University of Tokyo, The University of Osaka, and RIKEN

  15. Gauss-Newton Accuracy and Indefinite Hessians: Uniform Coexistence in Low-Cost Sets

    Oct 7, 2026Kihun Rhee, Hanjoon ByunGauss-Newton OptimizationSecond-Order Optimization

  16. Convex-Concave Reinforcement Learning

    Oct 6, 2026Shripad V. Deshmukh, Yaswanth Chittepu, Dhawal Gupta +2Reinforcement LearningPolicy Gradient Methods

    University of Massachusetts · Institute of Foundation Models

  17. Robust Local Optimization Done Right

    Oct 5, 2026James Pritts, Kevin KöserRelative Pose EstimationNonconvex Optimization

    Kiel University, Kiel, Germany

  18. Learn Feasibility Once, Optimize All Objectives: Derivative-Free Diffusion Models for Chance-Constrained Programming

    Oct 2, 2026Ziwen Liu, Yan Liu, Congying Han +3Chance-Constrained OptimizationDiffusion Models

    School of Mathematical Sciences, Beijing University of Posts and Telecommunications · School of Statistics and Data Science, Nankai University · School of Mathematical Sciences, University of the Chinese Academy of Sciences +1

  19. SoftServe: A Scalable Quasi-Newton Method for Deep Learning

    Oct 1, 2026Joohwan Ko, Tetiana Parshakova, Diana Cai +1Deep Learning OptimizationSecond-Order Optimization

    University of Massachusetts Amherst · CCM, Flatiron Institute · Cornell University

  20. Removing spurious minima for planar features by skip connections

    Oct 1, 2026Jakob Paul Zimmermann, Andrei Balakin, Moritz Grillo +1Shallow Neural NetworksReLU Neural Networks

    Freie Universität Berlin · Technische Universität Berlin

  21. Generalized Geometry Block Proximal Linearized Method for Multiblock Nonconvex and Nonsmooth Optimization

    Sep 30, 2026Weifeng YangNonconvex OptimizationConstrained Optimization

  22. Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing

    Sep 29, 2026Eugene Agyei-Kodie, Longxiu Huang, Shuang Li +1Nonconvex OptimizationOptimization Convergence Analysis

    Department of Mathematics, Michigan State University, 619 Red Cedar, East Lansing, 48824, MI, USA. · Department of Computational Mathematics, Science and Engineering, Michigan State University, 428 S Shaw Ln, East Lansing, 48824, MI, USA. · Department of Electrical and Computer Engineering, Iowa State University, 2520 Osborn Dr, Ames, 50011, IA, USA.

  23. DCEmbed: Scalable Optimization over Neural Surrogates

    Sep 27, 2026Akshay Sreekumar, Nicolas Christianson, Priya L. Donti +2Neural Surrogate ModelingSurrogate-Assisted Optimization

    Stanford University Stanford, CA, USA · Johns Hopkins University Baltimore, MD, USA · Massachusetts Institute of Technology Cambridge, MA, USA

  24. lapanda: A Matrix-Free Differentiable Solver for Nonconvex Constrained Optimization Layers

    Sep 27, 2026Yuankun Chen, Zifei Nie, Kangyu Lin +2Differentiable ProgrammingNonconvex Optimization

    School of Artificial Intelligence, Jilin University, China · Graduate School of Informatics, Kyoto University, JPN · Department of Civil and Systems Engineering, Johns Hopkins University, USA

  25. Orthogonal Witness Control for Muon Optimization via Sigmoid Spectral Reshaping

    Sep 27, 2026Dat Phi Van, Ngo Vu Minh, Tuc Nguyen +3Neural Network OptimizationSpectral Optimization

    Center for AI Research, VinUniversity, Hanoi, Vietnam · Indiana University, Bloomington, IN, USA · Monash University, Clayton, VIC, Australia

  26. Robust Game-theoretic Motion Planning over Extended Time Horizons

    Sep 26, 2026Bennet Outland, Vishala AryaMotion PlanningConstrained Motion Planning

    Smead Aerospace Engineering and Sciences Department University of Colorado Boulder Boulder, USA

  27. Transformer-Informed Trajectory Optimization for Relative Motion in Cislunar Orbits

    Sep 21, 2026Walter J. Manuel, Yuji Takubo, Simone D'AmicoTrajectory OptimizationSpacecraft Rendezvous and Proximity Operations

    Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305

  28. Near-Optimal Nonconvex Matrix Completion

    Sep 15, 2026Jian-Feng Cai, Xiliang Lu, Juntao YouRiemannian OptimizationNonconvex Optimization

    Department of Mathematics, Hong Kong University of Science and Technology. · School of Mathematics and Statistics, Hubei Center for Applied Mathematics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China. · School of Artificial Intelligence, Hubei Center for Applied Mathematics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China.

  29. Robust low-rank tensor completion via factorized weighted tensor schatten-p norm minimization

    Sep 13, 2026Binghao Wang, Feng Zhang, Wendong Wang +1Tensor CompletionTensor Decomposition

    School of Mathematics and Statistics, Southwest University, Chongqing 400715, China · College of Artificial Intelligence, Southwest University, Chongqing 400715, China

  30. Nonsmooth Optimization via Orthogonalized Momentum

    Sep 12, 2026Lexiao Lai, Tianyi Lin, Jiayu ZhangMuon OptimizerNonconvex Optimization

    Department of Mathematics, The University of Hong Kong · Department of Industrial Engineering and Operations Research Columbia University