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In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…

Machine Learning · Statistics 2014-06-19 Ziming Zhang , Venkatesh Saligrama

This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…

Optimization and Control · Mathematics 2020-01-22 Mohammad S. Alkousa

Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…

Optimization and Control · Mathematics 2026-02-17 Xiaozhe Hu , Sara Pollock , Zhongqin Xue , Yunrong Zhu

We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex function whose subgradients are estimated under heavy-tailed noise. Existing work often employs…

Optimization and Control · Mathematics 2025-10-14 Chuan He , Zhaosong Lu

Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…

Optimization and Control · Mathematics 2023-11-20 Alessandro Scagliotti , Piero Colli Franzone

Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most…

Machine Learning · Computer Science 2020-06-16 Yuan Gao , Christian Kroer , Donald Goldfarb

In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the…

We consider a class of structured, nonconvex, nonsmooth optimization problems under orthogonality constraints, where the objectives combine a smooth function, a nonsmooth concave function, and a nonsmooth weakly convex function. This class…

Optimization and Control · Mathematics 2025-01-14 Ganzhao Yuan

This paper addresses the distributed stochastic minimax optimization problem subject to stochastic constraints. We propose a novel first-order Softmax-Weighted Switching Gradient method tailored for federated learning. Under full client…

Machine Learning · Computer Science 2026-03-09 Zhankun Luo , Antesh Upadhyay , Sang Bin Moon , Abolfazl Hashemi

We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…

Optimization and Control · Mathematics 2016-08-26 Zeyuan Allen-Zhu , Elad Hazan

The optimistic gradient method has seen increasing popularity for solving convex-concave saddle point problems. To analyze its iteration complexity, a recent work [arXiv:1906.01115] proposed an interesting perspective that interprets this…

Optimization and Control · Mathematics 2024-01-11 Ruichen Jiang , Aryan Mokhtari

First-order methods with momentum such as Nesterov's fast gradient method are very useful for convex optimization problems, but can exhibit undesirable oscillations yielding slow convergence rates for some applications. An adaptive…

Optimization and Control · Mathematics 2019-06-14 Donghwan Kim , Jeffrey A. Fessler

We propose a general scheme for solving convex and non-convex optimization problems on manifolds. The central idea is that, by adding a multiple of the squared retraction distance to the objective function in question, we "convexify" the…

Computation · Statistics 2020-10-20 Lizhen Lin , Bayan Saparbayeva , Michael Minyi Zhang , David B. Dunson

We study the problem of minimizing a $m$-weakly convex and possibly nonsmooth function. Weak convexity provides a broad framework that subsumes convex, smooth, and many composite nonconvex functions. In this work, we propose a…

Optimization and Control · Mathematics 2025-09-04 Feng-Yi Liao , Yang Zheng

In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…

Optimization and Control · Mathematics 2020-06-05 Vando A. Adona , Max L. N. Gonçalves

We present adaptive gradient methods (both basic and accelerated) for solving convex composite optimization problems in which the main part is approximately smooth (a.k.a. $(\delta, L)$-smooth) and can be accessed only via a (potentially…

Optimization and Control · Mathematics 2024-06-11 Anton Rodomanov , Xiaowen Jiang , Sebastian Stich

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

Recently, many variance reduced stochastic alternating direction method of multipliers (ADMM) methods (e.g.\ SAG-ADMM, SDCA-ADMM and SVRG-ADMM) have made exciting progress such as linear convergence rates for strongly convex problems.…

Machine Learning · Computer Science 2017-07-12 Yuanyuan Liu , Fanhua Shang , James Cheng

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…

Optimization and Control · Mathematics 2024-02-01 Digvijay Boob , Qi Deng , Guanghui Lan

The work is devoted to the construction of efficient and applicable to real tasks first-order methods of convex optimization, that is, using only values of the target function and its derivatives. Construction uses OGM-G, fast gradient…

Optimization and Control · Mathematics 2020-09-10 Nikita Pletnev