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This paper develops a new parameter-free restarted method, namely RPF-SFISTA, and a new parameter-free aggressive regularization method, namely A-REG, for solving strongly convex and convex composite optimization problems, respectively.…

Optimization and Control · Mathematics 2024-10-15 Arnesh Sujanani , Renato D. C. Monteiro

In this technical note, we are concerned with the problem of solving variational inequalities with improved convergence rates. Motivated by Nesterov's accelerated gradient method for convex optimization, we propose a Nesterov's accelerated…

Optimization and Control · Mathematics 2022-12-21 Shaolin Tan , Jinhu Lu

This paper considers the problem of understanding the behavior of a general class of accelerated gradient methods on smooth nonconvex functions. Motivated by some recent works that have proposed effective algorithms, based on Polyak's heavy…

Optimization and Control · Mathematics 2026-04-07 Rishabh Dixit , Mert Gurbuzbalaban , Waheed U. Bajwa

We develop a novel optimistic gradient-type algorithmic framework, combining both Nesterov's acceleration and variance-reduction techniques, to solve a class of generalized equations involving possibly nonmonotone operators in data-driven…

Optimization and Control · Mathematics 2025-08-26 Quoc Tran-Dinh , Nghia Nguyen-Trung

In this paper, we propose a unified view of gradient-based algorithms for stochastic convex composite optimization by extending the concept of estimate sequence introduced by Nesterov. More precisely, we interpret a large class of…

Machine Learning · Statistics 2020-09-07 Andrei Kulunchakov , Julien Mairal

A significant milestone in modern gradient-based optimization was achieved with the development of Nesterov's accelerated gradient descent (NAG) method. This forward-backward technique has been further advanced with the introduction of its…

Optimization and Control · Mathematics 2024-04-10 Bowen Li , Bin Shi , Ya-xiang Yuan

In the Euclidean setting, the proximal gradient method and its accelerated variants are a class of efficient algorithms for optimization problems with decomposable objective. In this paper, we develop a Riemannian proximal gradient method…

Optimization and Control · Mathematics 2021-06-01 Wen Huang , Ke Wei

Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization…

Machine Learning · Statistics 2016-09-13 Xiyu Yu , Dacheng Tao

Despite their frequent slow convergence, proximal gradient schemes are widely used in large-scale optimization tasks due to their tremendous stability, scalability, and ease of computation. In this paper, we develop and investigate a…

Computation · Statistics 2025-08-19 Nicholas C. Henderson , Ravi Varadhan

The most popular first-order accelerated black-box methods for solving large-scale convex optimization problems are the Fast Gradient Method (FGM) and the Fast Iterative Shrinkage Thresholding Algorithm (FISTA). FGM requires that the…

Optimization and Control · Mathematics 2021-09-29 Mihai I. Florea , Sergiy A. Vorobyov

In this work we introduce a new optimisation method called SAGA in the spirit of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA improves on the theory behind SAG…

Machine Learning · Computer Science 2014-12-17 Aaron Defazio , Francis Bach , Simon Lacoste-Julien

This paper proposes an accelerated proximal stochastic variance reduced gradient (ASVRG) method, in which we design a simple and effective momentum acceleration trick. Unlike most existing accelerated stochastic variance reduction methods…

Machine Learning · Computer Science 2018-11-20 Fanhua Shang , Licheng Jiao , Kaiwen Zhou , James Cheng , Yan Ren , Yufei Jin

In the paper, we propose a class of faster adaptive Gradient Descent Ascent (GDA) methods for solving the nonconvex-strongly-concave minimax problems by using the unified adaptive matrices, which include almost all existing coordinate-wise…

Optimization and Control · Mathematics 2023-02-22 Feihu Huang , Xidong Wu , Zhengmian Hu

Gradient restarting has been shown to improve the numerical performance of accelerated gradient methods. This paper provides a mathematical analysis to understand these advantages. First, we establish global linear convergence guarantees…

Optimization and Control · Mathematics 2025-05-28 Chenglong Bao , Liang Chen , Jiahong Li , Zuowei Shen

Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…

Optimization and Control · Mathematics 2023-06-05 Hongyi Li , Zhen Peng , Chengwei Pan , Di Zhao

Nesterov's accelerated gradient descent method (AGD) is a seminal deterministic first-order method known to achieve the optimal order of iteration complexity for solving convex smooth optimization problems. Two distinct sequences of…

Optimization and Control · Mathematics 2026-03-10 Yan Wu , Yipeng Zhang , Lu Liu , Yuyuan Ouyang

This work proposes an Accelerated Primal-Dual Fixed-Point (APDFP) method that employs Nesterov type acceleration to solve composite problems of the form min f(x) + g(Bx), where g is nonsmooth and B is a linear operator. The APDFP features…

Optimization and Control · Mathematics 2025-11-04 Ya-Nan Zhu

Nesterov's accelerated gradient methods (AGM) have been successfully applied in many machine learning areas. However, their empirical performance on training max-margin models has been inferior to existing specialized solvers. In this…

Machine Learning · Computer Science 2010-11-03 Xinhua Zhang , Ankan Saha , S. V. N. Vishwanathan

We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster…

Optimization and Control · Mathematics 2020-01-07 Ashia Wilson , Lester Mackey , Andre Wibisono

We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…

Optimization and Control · Mathematics 2015-10-27 Hongzhou Lin , Julien Mairal , Zaid Harchaoui