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. Shuffling the Stochastic Mirror Descent via Dual Lipschitz Continuity and Kernel Conditioning

    Mar 17, 2026Junwen Qiu, Leilei Mei, Junyu ZhangRandom ReshufflingStochastic Optimization

    Industrial Systems Engineering and Management, National University of Singapore

  2. Muon Converges under Heavy-Tailed Noise: Nonconvex Hölder-Smooth Empirical Risk Minimization

    Mar 16, 2026Hideaki IidukaNonconvex Stochastic OptimizationMuon Optimizer

    Department of Computer Science Meiji University 1-1-1 Higashimita, Tama-ku, Kawasaki-shi, Kanagawa 214-8571 Japan

  3. Probabilistic Gaussian Homotopy: A Probability-Space Continuation Framework for Nonconvex Optimization

    Mar 13, 2026Eshed Gal, Samy Wu Fung, Eldad HaberNonconvex OptimizationStochastic Optimization

    University of British Columbia, Vancouver, BC, Canada · Colorado School of Mines, Golden, CO, USA

  4. Quantum mechanical framework for quantization-based optimization: from Gradient flow to Schroedinger equation

    Mar 12, 2026Jinwuk Seok, Changsik ChoHJB EquationsGlobal Optimization

    On-Device AIM Research Section AIC Research Lab, ETRI Daejeon, Rep. Korea

  5. ADMM-based Continuous Trajectory Optimization in Graphs of Convex Sets

    Mar 11, 2026Lukas Pries, Jon Arrizabalaga, Zachary Manchester +1Trajectory OptimizationAlternating 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

  6. Parallel-in-Time Nonlinear Optimal Control via GPU-native Sequential Convex Programming

    Mar 11, 2026Yilin Zou, Zhong Zhang, Maxime Robic +1Optimal ControlGPU Acceleration

    School of Aerospace Engineering, Tsinghua University, 100084 Beijing, China. · Department of Aerospace Science and Technology, Politecnico di Milano, 20156 Milan, Italy.

  7. Compressed Proximal Federated Learning for Non-Convex Composite Optimization on Heterogeneous Data

    Mar 8, 2026Pu Qiu, Chen Ouyang, Yongyang Xiong +3Error FeedbackFederated Learning

    School of Intelligent Systems Engineering, Sun Yat-Sen University, Shenzhen 518107, P.R China. · Department of Automation, Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China. · Department of Mechanical Engineering, University of Victoria, Victoria, BC V8W 2Y2, Canada.

  8. Omni-Masked Gradient Descent: Memory-Efficient Optimization via Mask Traversal with Improved Convergence

    Mar 6, 2026Hui Yang, Tao Ren, Jinyang Jiang +2Gradient DescentMemory-Efficient Training

    1Guanghua School of Management, Peking University · 2Wangxuan Institute of Computer Technology, Peking University.

  9. Compact Lifted Relaxations for Low-Rank Optimization

    Mar 5, 2026Ryan Cory-Wright, Jean PauphiletSemidefinite ProgrammingNonconvex Optimization

    Department of Analytics, Marketing and Operations, Imperial Business School, London, UK · Management Science and Operations, London Business School, London, UK

  10. Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penalties

    Mar 1, 2026Takanobu Furuhashi, Hiroki Kuroda, Masahiro Yukawa +3Structured SparsityNonconvex Optimization

    Nagoya Institute of Technology, Nagoya, Japan · Nagaoka University of Technology, Niigata, Japan · Keio University, Yokohama, Japan +1

  11. On the Stability of Nonlinear Dynamics in GD and SGD: Beyond Quadratic Potentials

    Feb 16, 2026Rotem Mulayoff, Sebastian U. StichGradient Descent DynamicsStochastic Gradient Descent

    CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

  12. Advances in Global Solvers for 3D Vision

    Feb 16, 2026Zhenjun Zhao, Heng Yang, Bangyan Liao +7Convex RelaxationGlobal Optimization

    University of Zaragoza, Zaragoza, Spain. · Harvard University, Cambridge, MA, USA. · Westlake University, Hangzhou, China. +3

  13. BalLOT: Balanced kk-means clustering with optimal transport

    Dec 5, 2025Wenyan Luo, Dustin G. MixonClusteringNonconvex Optimization

    Department of Mathematics, The Ohio State University, Columbus, Ohio, USA · Translational Data Analytics Institute, The Ohio State University, Columbus, Ohio, USA

  14. On the Condition Number Dependency in Bilevel Optimization

    Nov 27, 2025Lesi Chen, Jingzhao ZhangOracle ComplexityNonconvex Optimization

    IIIS, Tsinghua University

  15. Anytime-Feasible First-Order Optimization via Safe Sequential QCQP

    Nov 24, 2025Jiarui Wang, Mahyar FazlyabConstrained OptimizationNonconvex Optimization

    Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD 21218 USA

  16. Power Homotopy for Zeroth-Order Non-Convex Optimizations

    Nov 17, 2025Chen XuZeroth-Order OptimizationNonconvex Optimization

    Department of Engineering, Shenzhen MSU-BIT University, China.

  17. Disciplined Biconvex Programming

    Nov 3, 2025Hao Zhu, Joschka BoedeckerNonconvex OptimizationConstrained Optimization

    IMBIT//BrainLinks-BrainTools · Department of Computer Science, University of Freiburg

  18. The Optimization Landscape of Carathéodory Decomposition of Toeplitz Covariances

    Nov 3, 2025Daniel Busbib, Ami WieselNonconvex OptimizationMatrix Optimization

    School of Computer Science and Engineering, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

  19. Stochastic Difference-of-Convex Optimization with Momentum

    Oct 20, 2025El Mahdi Chayti, Martin JaggiNonconvex OptimizationNonconvex Stochastic Optimization

    Machine Learning and Optimization Laboratory (MLO), EPFL

  20. Smooth Quasar-Convex Optimization with Constraints

    Oct 2, 2025David Martínez-RubioRiemannian OptimizationNonconvex Optimization

    IMDEA Software Institute · Madrid, Spain

  21. Convergence Analysis of the ProbAbilistic Gradient Estimator Algorithm for Weakly Convex Finite-Sum Optimization

    Aug 31, 2025Laurent Condat, Peter RichtárikStochastic OptimizationNonconvex Stochastic Optimization

    King Abdullah University of Science and Technology (KAUST) Thuwal, Kingdom of Saudi Arabia

  22. Douglas-Rachford Splitting for Group-Sparse Feedback Linear-Quadratic Control

    Jul 26, 2025Lechen Feng, Xun Li, Yuan-Hua NiDistributed OptimizationDistributed Control

    Department of Applied Mathematics, The Hong Kong Polytechnic University, China · College of Artificial Intelligence, Nankai University, Tianjin, China

  23. Linearly Convergent Algorithms for Nonsmooth Problems with Unknown Smooth Regions

    Jul 25, 2025Zhe Zhang, Suvrit SraNonsmooth Convex OptimizationNonconvex Optimization

    School of Industrial Engineering, Purdue University, USA · Department of Mathematics, CIT, TU Munich, Germany

  24. Quantum Speedups for Sampling and Non-convex Optimization with Stochastic Oracles

    Apr 4, 2025Guneykan Ozgul, Xiantao Li, Mehrdad Mahdavi +1Markov Chain Monte CarloStochastic 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

  25. Convergence of Sharpness-Aware Minimization Algorithms using Increasing Batch Size and Decaying Learning Rate

    Sep 16, 2024Hinata Harada, Hideaki IidukaSharpness-Aware MinimizationNonconvex Optimization

    Meiji University, Japan

  26. Accelerated Stochastic Min-Max Optimization Based on Bias-corrected Momentum

    Jun 18, 2024Haoyuan Cai, Sulaiman A. Alghunaim, Ali H. SayedMomentum MethodsNonconvex Stochastic Optimization

    Ecole Polytechnique Fédérale de Lausanne, Switzerland · Kuwait University, Kuwait

  27. Accelerated Gradient Methods for Nonconvex Optimization: Escape Trajectories From Strict Saddle Points and Convergence to Local Minima

    Jul 13, 2023Rishabh Dixit, Mert Gurbuzbalaban, Waheed U. BajwaNonconvex OptimizationAccelerated Gradient Methods

    Department of Electrical and Computer Engineering, Rutgers University–New Brunswick, NJ 08854 USA · Departments of Electrical & Computer Engineering, Management Science and Information Systems, and Statistics, Rutgers University–New Brunswick, NJ 08854 USA · Departments of Electrical & Computer Engineering and Statistics, Rutgers University–New Brunswick, NJ 08854 USA