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We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…

Optimization and Control · Mathematics 2026-04-16 Javier I. Madariaga

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

Machine Learning · Computer Science 2022-10-04 Ayano Kaneda , Osman Akar , Jingyu Chen , Victoria Kala , David Hyde , Joseph Teran

We consider the problem of minimizing a finite sum of convex functions subject to the set of minimizers of a convex differentiable function. In order to solve the problem, an algorithm combining the incremental proximal gradient method with…

Optimization and Control · Mathematics 2020-04-21 Nimit Nimana , Narin Petrot

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…

Machine Learning · Computer Science 2011-12-02 Mark Schmidt , Nicolas Le Roux , Francis Bach

In this paper, we consider a class of finite-sum convex optimization problems whose objective function is given by the summation of $m$ ($\ge 1$) smooth components together with some other relatively simple terms. We first introduce a…

Optimization and Control · Mathematics 2015-10-27 Guanghui Lan , Yi Zhou

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

Optimization and Control · Mathematics 2013-02-14 Ion Necoara , Andrei Patrascu

In this paper we develop random block coordinate gradient descent methods for minimizing large scale linearly constrained separable convex problems over networks. Since we have coupled constraints in the problem, we devise an algorithm that…

Optimization and Control · Mathematics 2015-12-14 I. Necoara , Yu. Nesterov , F. Glineur

In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…

Optimization and Control · Mathematics 2014-10-01 Ion Necoara , Valentin Nedelcu

In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…

Optimization and Control · Mathematics 2024-01-10 Flavia Chorobura , Ion Necoara

We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an…

Optimization and Control · Mathematics 2014-07-07 Qihang Lin , Zhaosong Lu , Lin Xiao

We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…

Optimization and Control · Mathematics 2014-03-20 Lin Xiao , Tong Zhang

A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…

Methodology · Statistics 2018-12-18 Jon Cockayne , Chris Oates , Ilse Ipsen , Mark Girolami

The purpose of this paper is to introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M…

Optimization and Control · Mathematics 2024-06-21 Anteneh Getachew Gebrie

We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed…

Optimization and Control · Mathematics 2013-03-12 Nicolas Le Roux , Mark Schmidt , Francis Bach

This article investigates a distributed aggregative optimization problem subject to coupled affine inequality constraints, in which local objective functions depend not only on their own decision variables but also on an aggregation of all…

Optimization and Control · Mathematics 2023-06-13 Kaixin Du , Min Meng

We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…

Optimization and Control · Mathematics 2024-02-14 Alberto De Marchi

We provide new insight into a {\em generalized conditional subgradient} algorithm and a {\em generalized mirror descent} algorithm for the convex minimization problem \[ \min_x \; \{f(Ax) + h(x)\}.\] As Bach showed in [{\em SIAM J. Optim.},…

Optimization and Control · Mathematics 2019-06-04 Javier Pena

In this paper, a new variant of accelerated gradient descent is proposed. The pro-posed method does not require any information about the objective function, usesexact line search for the practical accelerations of convergence, converges…

Optimization and Control · Mathematics 2019-05-14 Yurii Nesterov , Alexander Gasnikov , Sergey Guminov , Pavel Dvurechensky

This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…

Optimization and Control · Mathematics 2024-07-23 Yao Yao , Qihang Lin , Tianbao Yang

We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…

Optimization and Control · Mathematics 2019-07-12 Reinier Díaz Millán , Majela Pentón Machado