English
Related papers

Related papers: Inexact Coordinate Descent: Complexity and Precond…

200 papers

Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models…

Optimization and Control · Mathematics 2023-04-28 V. S. Amaral , R. Andreani , E. G. Birgin , D. S. Marcondes , J. M. Martínez

We study the worst-case behavior of Block Coordinate Descent (BCD) type algorithms for unconstrained minimization of coordinate-wise smooth convex functions. This behavior is indeed not completely understood, and the practical success of…

Optimization and Control · Mathematics 2025-07-23 Yassine Kamri , François Glineur , Julien M. Hendrickx , Ion Necoara

In this paper, we study the randomized distributed coordinate descent algorithm with quantized updates. In the literature, the iteration complexity of the randomized distributed coordinate descent algorithm has been characterized under the…

Machine Learning · Statistics 2017-01-23 Mostafa El Gamal , Lifeng Lai

In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework,…

Optimization and Control · Mathematics 2020-12-17 Pavel Dvurechensky , Alexander Gasnikov , Alexander Tiurin , Vladimir Zholobov

This paper considers the problems of unconstrained minimization of large scale smooth convex functions having block-coordinate-wise Lipschitz continuous gradients. The block coordinate descent (BCD) method are among the first optimization…

Optimization and Control · Mathematics 2016-08-18 Ziqiang Shi , Rujie Liu

Coordinate descent algorithms are widely used in machine learning and large-scale data analysis due to their strong optimality guarantees and impressive empirical performance in solving non-convex problems. In this work, we introduce Block…

Optimization and Control · Mathematics 2024-12-17 Zhijie Yuan , Ganzhao Yuan , Lei Sun

In this paper we propose a distributed version of a randomized block-coordinate descent method for minimizing the sum of a partially separable smooth convex function and a fully separable non-smooth convex function. Under the assumption of…

Optimization and Control · Mathematics 2015-11-23 Ion Necoara , Dragos Clipici

Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…

Optimization and Control · Mathematics 2025-12-05 Ting Li , Deren Han , Tanxing Wang , Xingju Cai

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…

Machine Learning · Computer Science 2020-06-09 Cong Ma , Kaizheng Wang , Yuejie Chi , Yuxin Chen

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

In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under generic assumptions, we prove that the algorithm iterate…

Optimization and Control · Mathematics 2022-12-01 Ziang Chen , Yingzhou Li , Jianfeng Lu

We propose and analyze a new parallel coordinate descent method---`NSync---in which at each iteration a random subset of coordinates is updated, in parallel, allowing for the subsets to be chosen non-uniformly. We derive convergence rates…

Machine Learning · Statistics 2013-10-15 Peter Richtárik , Martin Takáč

In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…

Optimization and Control · Mathematics 2024-01-11 Angelia Nedich , Ion Necoara

We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…

Optimization and Control · Mathematics 2018-01-30 Anastasia Bayandina , Pavel Dvurechensky , Alexander Gasnikov , Fedor Stonyakin , Alexander Titov

As the number of samples and dimensionality of optimization problems related to statistics an machine learning explode, block coordinate descent algorithms have gained popularity since they reduce the original problem to several smaller…

Machine Learning · Computer Science 2016-06-24 Rémi Flamary , Alain Rakotomamonjy , Gilles Gasso

We consider the classical gradient descent algorithm with constant stepsizes, where some error is introduced in the computation of each gradient. More specifically, we assume some relative bound on the inexactness, in the sense that the…

Optimization and Control · Mathematics 2025-09-12 Pierre Vernimmen , François Glineur

We study the problem of minimizing the sum of potentially non-differentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the…

Optimization and Control · Mathematics 2021-02-17 Yankai Lin , Iman Shames , Dragan Nesic

Block-coordinate descent (BCD) is the method of choice to solve numerous large scale optimization problems, however their theoretical study for non-convex optimization, has received less attention. In this paper, we present a new…

Machine Learning · Computer Science 2026-01-30 Guillaume Lauga

In this work we propose a distributed randomized block coordinate descent method for minimizing a convex function with a huge number of variables/coordinates. We analyze its complexity under the assumption that the smooth part of the…

Optimization and Control · Mathematics 2015-07-21 Jakub Marecek , Peter Richtarik , Martin Takac

Block coordinate descent (BCD) methods approach optimization problems by performing gradient steps along alternating subgroups of coordinates. This is in contrast to full gradient descent, where a gradient step updates all coordinates…

Numerical Analysis · Mathematics 2019-07-29 Simon Rabanser , Lukas Neumann , Markus Haltmeier