Nonsmooth Convex Optimization

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Overview

It seeks reliable minimizers when losses have kinks or constraints, as in robust, composite, and distributed learning, where ordinary gradient methods may not apply. Core tools include subgradient and proximal-point methods, bundle methods, three-operator splitting, primal-dual and gossip schemes, and stochastic variants using clipping or variance control. Theory studies convergence and oracle complexity on composite problems, networked objectives, and noisy or information-limited oracles, with stronger rates under conditions such as quadratic growth, sharpness, or strong convexity. A central tension is that guarantees depend strongly on geometry and noise assumptions, while cheaper, communication-limited, or privacy-preserving updates can require more iterations or weaker rates.

Latest papers

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22 papers1 paper in the last four weeks, down 75% on the four weeks before. 0.0% of all new papers.

  1. Last-Iterate Convergence of Clipped SGD with Linear Decay

    Oct 13, 2026Wei Jiang, Haomin Bai, Zechao LiLast-Iterate ConvergenceStochastic Gradient Descent

    School of Computer Science and Engineering, Nanjing University of Science and Technology · National Key Laboratory for Novel Software Technology, Nanjing University

  2. Complexities of Weak Proximal Oracle Methods for Composite Convex Optimization

    Sep 21, 2026Dan GarberOracle ComplexityOptimization Convergence Analysis

    Faculty of Data and Decision Sciences Technion - Israel Institute of Technology

  3. Stable Movement for Nondual Lipschitz Convex Optimization: Efficiency and Nearly Optimal Oracle Rates

    Sep 17, 2026David Martínez-Rubio, Cristóbal GuzmánConstrained OptimizationNonsmooth Convex Optimization

    IMDEA Software Institute, Madrid, Spain · Institute for Mathematical and Computational Engineering, Faculty of Mathematics and School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile

  4. The First-Order Oracle Complexity of Lipschitz Convex Optimization in Nondual Settings

    Sep 17, 2026David Martínez-Rubio, Brian Bullins, Cristóbal Guzmán +1Nonsmooth Convex Optimization

    IMDEA Software Institute, Madrid, Spain · Purdue University, West Lafayette, IN, USA · Institute for Mathematical and Computational Engineering, Faculty of Mathematics and School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile +1

  5. 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

  6. Active-Trace Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling

    Aug 13, 2026Yuchen Xin, Zhihua ZhangLangevin DynamicsSample Complexity

    School of Mathematical Sciences, Peking University

  7. Finding a stationary point of a stochastic convex problem

    Jul 8, 2026Felipe Areces, John Duchi, Malo SommersStochastic Optimization ConvergenceNonsmooth Convex Optimization

    Stanford University

  8. Decentralized Stochastic Subgradient-type Methods with Communication Compression for Nonsmooth Nonconvex Optimization

    Jul 2, 2026Siyuan Zhang, Nachuan Xiao, Xin LiuStochastic OptimizationNonconvex Optimization

  9. New Bounds for the Last Iterate of the Stochastic subGradient Method

    Jun 23, 2026Guglielmo Beretta, Tommaso Cesari, Roberto Colomboni +1Stochastic OptimizationLast-Iterate Convergence

    Department of Computer Science, Aarhus University, Aarhus, Denmark · School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Canada · School of Mathematics, University of Bristol, Bristol, United Kingdom

  10. Adam Converges in Nonsmooth Nonconvex Optimization

    Jun 21, 2026Zijian LiuHeavy-Tailed NoiseNonconvex Optimization

    Department of Technology, Operations, and Statistics Leonard N. Stern School of Business New York University New York, NY 10012, USA

  11. Convergence of Spectral Descent for Non-smooth Optimization

    May 26, 2026Yixuan Yang, Yuqing He, Song LiMuon OptimizerNonsmooth Convex Optimization

    School of Mathematical Sciences, Zhejiang University, Hangzhou, China

  12. Zeroth-Order Nonconvex Nonsmooth Optimization with Heavy-Tailed Noise

    May 23, 2026Zhuanghua Liu, Luo LuoStochastic OptimizationGradient Clipping

  13. Stochastic Non-Smooth Convex Optimization with Unbounded Gradients

    May 15, 2026Dmitry KovalevStochastic OptimizationGradient Clipping

    Yandex Research

  14. Nonsmooth Set-Gradient Ascent to the Pareto Front via Layered Hypervolume and Magnitude Indicators

    May 13, 2026Michael T. M. EmmerichMulti-Objective OptimizationPareto Optimization

    Faculty of Information Technology, University of Jyväskylä, Finland

  15. Parameterized Complexity of Stationarity Testing for Piecewise-Affine Functions and Shallow CNN Losses

    May 11, 2026Yuhan YeShallow Neural NetworksNonconvex Optimization

    MIT

  16. Adaptive Decentralized Composite Optimization via Three-Operator Splitting

    Feb 19, 2026Xiaokai Chen, Ilya Kuruzov, Gesualdo ScutariDecentralized OptimizationNonsmooth Convex Optimization

    Edwardson School of Industrial Engineering, Purdue University, West Lafayette, IN 47906 USA

  17. Local adapt-then-combine algorithms for distributed nonsmooth optimization: Achieving provable communication acceleration

    Feb 18, 2026Luyao Guo, Xinli Shi, Wenying Xu +1Distributed OptimizationNonsmooth Convex Optimization

    School of Computer Science and Engineering, Suzhou University of Technology, Suzhou 215500, China · School of Mathematics, Southeast University, Nanjing 210096, China · School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China

  18. Fast and Efficient Asynchronous Gossip Algorithm for Robust and Non-Smooth Convex Decentralized Learning

    Jan 28, 2026Anna van Elst, Olivier Fercoq, Igor Colin +1Decentralized LearningNonsmooth Convex Optimization

    LTCI, Télécom Paris, Institut Polytechnique de Paris

  19. On the Gradient Complexity of Private Optimization with Private Oracles

    Nov 17, 2025Michael Menart, Aleksandar NikolovQuery ComplexityOracle Complexity

    Department of Computer Science, University of Toronto, Vector Institute · Department of Computer Science, University of Toronto

  20. 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

  21. Towards Weaker Variance Assumptions for Stochastic Optimization

    Apr 14, 2025Ahmet Alacaoglu, Yura Malitsky, Stephen J. WrightStochastic OptimizationLast-Iterate Convergence

    Department of Mathematics, University of British Columbia · Faculty of Mathematics, University of Vienna · Department of Computer Sciences, University of Wisconsin–Madison

  22. NAG-GS: A Semi-Implicit Stochastic Optimizer with Large-Step Stability

    Sep 29, 2022Valentin Leplat, Daniil Merkulov, Aleksandr Katrutsa +3Stochastic OptimizationAccelerated Gradient Methods

    Skolkovo Institute of Science and Technology, Moscow, Russia · Moscow Institute of Physics and Technology, Moscow, Russia · AIRI, Moscow, Russia +1