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We study the linear convergence rates of the proximal gradient method for composite functions satisfying two classes of Polyak-{\L}ojasiewicz (PL) inequality: the PL inequality, the variant of PL inequality defined by the proximal map-based…

Optimization and Control · Mathematics 2025-07-01 Qingyuan Kong , Rujun Jiang , Yihan He

A very popular approach for solving stochastic optimization problems is the stochastic gradient descent method (SGD). Although the SGD iteration is computationally cheap and the practical performance of this method may be satisfactory under…

Optimization and Control · Mathematics 2017-06-21 Andrei Patrascu , Ion Necoara

Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type,…

Optimization and Control · Mathematics 2021-10-26 Aleksandr Beznosikov , Alexander Rogozin , Dmitry Kovalev , Alexander Gasnikov

Large-scale saddle-point problems arise in such machine learning tasks as GANs and linear models with affine constraints. In this paper, we study distributed saddle-point problems (SPP) with strongly-convex-strongly-concave smooth…

Optimization and Control · Mathematics 2022-10-04 Dmitriy Metelev , Alexander Rogozin , Alexander Gasnikov , Dmitry Kovalev

This paper focuses on solving a stochastic saddle point problem (SPP) under an overparameterized regime for the case, when the gradient computation is impractical. As an intermediate step, we generalize Same-sample Stochastic Extra-gradient…

Optimization and Control · Mathematics 2024-06-05 Ekaterina Statkevich , Sofiya Bondar , Darina Dvinskikh , Alexander Gasnikov , Aleksandr Lobanov

We study the convergence rate of gradient-based local search methods for solving low-rank matrix recovery problems with general objectives in both symmetric and asymmetric cases, under the assumption of the restricted isometry property.…

Optimization and Control · Mathematics 2022-03-10 Yingjie Bi , Haixiang Zhang , Javad Lavaei

In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…

Optimization and Control · Mathematics 2024-10-25 Md Abu Talhamainuddin Ansary

This paper focuses on the online gradient and proximal-gradient methods with stochastic gradient errors. In particular, we examine the performance of the online gradient descent method when the cost satisfies the Polyak-\L ojasiewicz (PL)…

Optimization and Control · Mathematics 2024-07-16 Seunghyun Kim , Liam Madden , Emiliano Dall'Anese

In the paper, we generalize the approach Gasnikov et. al, 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle, to the convex-concave saddle-point problem. The proposed approach works,…

Optimization and Control · Mathematics 2022-09-13 Aleksandr Beznosikov , Abdurakhmon Sadiev , Alexander Gasnikov

In this paper, we derive a new linear convergence rate for the gradient method with fixed step lengths for non-convex smooth optimization problems satisfying the Polyak-Lojasiewicz (PL) inequality. We establish that the PL inequality is a…

Optimization and Control · Mathematics 2022-04-05 Hadi Abbaszadehpeivasti , Etienne de Klerk , Moslem Zamani

Minimax optimization recently is widely applied in many machine learning tasks such as generative adversarial networks, robust learning and reinforcement learning. In the paper, we study a class of nonconvex-nonconcave minimax optimization…

Optimization and Control · Mathematics 2025-04-23 Feihu Huang , Chunyu Xuan , Xinrui Wang , Siqi Zhang , Songcan Chen

This paper addresses the generalized descent algorithm (DEAL) for minimizing smooth functions, which is analyzed under the Kurdyka-{\L}ojasiewicz (KL) inequality. In particular, the suggested algorithm guarantees a sufficient decrease by…

Optimization and Control · Mathematics 2025-11-14 Masoud Ahookhosh , Susan Ghaderi , Alireza Kabgani , Morteza Rahimi

This paper introduces a novel optimization algorithm designed for nonlinear least-squares problems. The method is derived by preconditioning the gradient descent direction using the Singular Value Decomposition (SVD) of the Jacobian. This…

Numerical Analysis · Mathematics 2026-02-11 Zhipeng Chang , Wenrui Hao , Nian Liu

In this paper, we focus on solving a class of constrained non-convex non-concave saddle point problems in a decentralized manner by a group of nodes in a network. Specifically, we assume that each node has access to a summand of a global…

Optimization and Control · Mathematics 2019-11-01 Weijie Liu , Aryan Mokhtari , Asuman Ozdaglar , Sarath Pattathil , Zebang Shen , Nenggan Zheng

This paper considers stochastic first-order algorithms for minimax optimization under Polyak--{\L}ojasiewicz (PL) conditions. We propose SPIDER-GDA for solving the finite-sum problem of the form $\min_x \max_y f(x,y)\triangleq \frac{1}{n}…

Optimization and Control · Mathematics 2026-03-17 Lesi Chen , Boyuan Yao , Luo Luo

When training neural networks with low-precision computation, rounding errors often cause stagnation or are detrimental to the convergence of the optimizers; in this paper we study the influence of rounding errors on the convergence of the…

Machine Learning · Statistics 2025-01-22 Lu Xia , Michiel E. Hochstenbach , Stefano Massei

Minimax optimization problems have attracted significant attention in recent years due to their widespread application in numerous machine learning models. To solve the minimax problem, a wide variety of stochastic optimization methods have…

Machine Learning · Computer Science 2024-06-12 Hongchang Gao

Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be…

Optimization and Control · Mathematics 2019-11-01 Maher Nouiehed , Maziar Sanjabi , Tianjian Huang , Jason D. Lee , Meisam Razaviyayn

This paper considers distributed optimization for minimizing the average of local nonconvex cost functions, by using local information exchange over undirected communication networks. To reduce the required communication capacity, we…

Optimization and Control · Mathematics 2025-03-03 Lei Xu , Xinlei Yi , Jiayue Sun , Yang Shi , Karl H. Johansson , Tao Yang

Adaptive gradient-descent optimizers are the standard choice for training neural network models. Despite their faster convergence than gradient-descent and remarkable performance in practice, the adaptive optimizers are not as well…

Machine Learning · Computer Science 2024-07-18 Kushal Chakrabarti , Mayank Baranwal