Nonconvex Optimization

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10 papers in the last four weeks, up 100% on the four weeks before. 0.1% of all new papers.

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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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Smooth Quasar-Convex Optimization with Constraints

David Martínez-Rubio

IMDEA Software Institute · Madrid, Spain

Riemannian Optimization Nonconvex Optimization Constrained Optimization

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Quasar-convex functions form a broad nonconvex class with applications to linear dynamical systems, generalized linear models, and Riemannian optimization, among others. Current nearly optimal algorithms work only in affine spaces due to the loss of one degree of freedom when working with general convex constraints. Obtaining an accelerated algorithm that makes nearly optimal

\widetilde{O}(1/(γ\sqrt{\varepsilon}))

first-order queries to a

γ

-quasar convex smooth function \emph{with constraints} was independently asked as an open problem in Martínez-Rubio (2022); Lezane, Langer, and Koolen (2024). In this work, we solve this question by designing an inexact accelerated proximal point algorithm that we implement using a first-order method achieving the aforementioned rate and, as a consequence, we improve the complexity of the accelerated geodesically Riemannian optimization solution in Martínez-Rubio (2022). We also analyze projected gradient descent and Frank-Wolfe algorithms in this constrained quasar-convex setting. To the best of our knowledge, our work provides the first analyses of first-order methods for quasar-convex smooth functions with general convex constraints.

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Latest papers 96

Smooth Quasar-Convex Optimization with Constraints

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

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

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

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

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