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We consider a distributed stochastic optimization problem that is solved by a decentralized network of agents with only local communication between neighboring agents. The goal of the whole system is to minimize a global objective function…

Optimization and Control · Mathematics 2022-11-10 Alexander Rogozin , Mikhail Bochko , Pavel Dvurechensky , Alexander Gasnikov , Vladislav Lukoshkin

Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…

Optimization and Control · Mathematics 2018-01-15 Shuoguang Yang , Mengdi Wang , Ethan X. Fang

This paper is devoted to the study of accelerated proximal gradient methods where the sequence that controls the momentum term doesn't follow Nesterov's rule. We propose a relaxed weak accelerated proximal gradient (R-WAPG) method, a…

Optimization and Control · Mathematics 2025-04-10 Hongda Li , Xianfu Wang

We develop an adaptive Nesterov accelerated proximal gradient (adaNAPG) algorithm for stochastic composite optimization problems, boosting the Nesterov accelerated proximal gradient (NAPG) algorithm through the integration of an adaptive…

Optimization and Control · Mathematics 2025-07-25 Dongxuan Zhu , Weihuan Huang , Caihua Chen

We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…

Optimization and Control · Mathematics 2017-03-03 Alfredo Iusem , Alejandro Jofré , Philip Thompson

Nesterov's accelerated gradient method (NAG) is widely used in problems with machine learning background including deep learning, and is corresponding to a continuous-time differential equation. From this connection, the property of the…

Optimization and Control · Mathematics 2022-04-05 Yasong Feng , Weiguo Gao

In this paper, we propose some accelerated methods for solving optimization problems under the condition of relatively smooth and relatively Lipschitz continuous functions with an inexact oracle. We consider the problem of minimizing the…

Optimization and Control · Mathematics 2024-11-27 O. S. Savchuk , M. S. Alkousa , A. S. Shushko , A. A. Vyguzov , F. S. Stonyakin , D. A. Pasechnyuk , A. V. Gasnikov

We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed…

Machine Learning · Statistics 2019-01-03 Courtney Paquette , Hongzhou Lin , Dmitriy Drusvyatskiy , Julien Mairal , Zaid Harchaoui

Current state-of-the-art analyses on the convergence of gradient descent for training neural networks focus on characterizing properties of the loss landscape, such as the Polyak-Lojaciewicz (PL) condition and the restricted strong…

Machine Learning · Computer Science 2024-01-08 Fangshuo Liao , Anastasios Kyrillidis

We propose a new family of subgradient- and gradient-based methods which converges with optimal complexity for convex optimization problems whose feasible region is simple enough. This includes cases where the objective function is…

Optimization and Control · Mathematics 2016-08-19 Masaru Ito , Mituhiro Fukuda

We consider distributed optimization in random networks where N nodes cooperatively minimize the sum \sum_{i=1}^N f_i(x) of their individual convex costs. Existing literature proposes distributed gradient-like methods that are…

Information Theory · Computer Science 2023-07-19 Dusan Jakovetic , Joao Xavier , Jose M. F. Moura

We introduce the continuized Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation…

Nesterov's accelerated gradient algorithm is derived from first principles. The first principles are founded on the recently-developed optimal control theory for optimization. This theory frames an optimization problem as an optimal control…

Optimization and Control · Mathematics 2023-09-12 I. M. Ross

This paper is concerned with convergence of stochastic gradient algorithms with momentum terms in the nonconvex setting. A class of stochastic momentum methods, including stochastic gradient descent, heavy ball, and Nesterov's accelerated…

Optimization and Control · Mathematics 2021-10-01 Zixuan Wang , Shanjian Tang

We propose a distributed method to solve a multi-agent optimization problem with strongly convex cost function and equality coupling constraints. The method is based on Nesterov's accelerated gradient approach and works over stochastically…

Optimization and Control · Mathematics 2020-12-17 Wicak Ananduta , Carlos Ocampo-Martinez , Angelia Nedić

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

Optimization and Control · Mathematics 2025-04-21 Spyridon Pougkakiotis , Dionysios S. Kalogerias

Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…

Optimization and Control · Mathematics 2018-02-28 Cong Fang , Yameng Huang , Zhouchen Lin

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 the article we have obtained some estimates of the rate of convergence for the recently proposed by Yu.E. Nesterov method of minimization of a convex Lipschitz-continuous function of two variables on a square with a fixed side. The…

Optimization and Control · Mathematics 2020-01-14 Dmitry A. Pasechnyuk , Fedor S. Stonyakin

We study the convergence of accelerated stochastic gradient descent for strongly convex objectives under the growth condition, which states that the variance of stochastic gradient is bounded by a multiplicative part that grows with the…

Optimization and Control · Mathematics 2023-11-01 You-Lin Chen , Sen Na , Mladen Kolar