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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 introduce a unified algorithmic framework, called proximal-like incremental aggregated gradient (PLIAG) method, for minimizing the sum of a convex function that consists of additive relatively smooth convex components and a proper lower…

Optimization and Control · Mathematics 2019-08-12 Hui Zhang , Yu-Hong Dai , Lei Guo , Wei Peng

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…

Optimization and Control · Mathematics 2017-06-20 Quang Van Nguyen , Olivier Fercoq , Volkan Cevher

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

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

Optimization and Control · Mathematics 2023-02-17 Jelena Diakonikolas , Cristóbal Guzmán

In a recent study, Ansary (Optim Methods Softw 38(3):570-590,2023) proposed a Newton-type proximal gradient method for nonlinear multiobjective optimization problems (NPGMO). However, the favorable convergence properties typically…

Optimization and Control · Mathematics 2023-08-22 Jian Chen , Xiaoxue Jiang , Liping Tang , Xinmin Yang

We consider the problem of minimizing the sum of an average function of a large number of smooth convex components and a general, possibly non-differentiable, convex function. Although many methods have been proposed to solve this problem…

Optimization and Control · Mathematics 2019-01-01 Le Thi Khanh Hien , Cuong V. Nguyen , Huan Xu , Canyi Lu , Jiashi Feng

In this paper we study a nonlinear dual space preconditioning approach for the relaxed Proximal Point Algorithm (PPA) with application to monotone and relatively cohypomonotone inclusions, called anisotropic PPA. The algorithm is an…

Optimization and Control · Mathematics 2025-12-30 Emanuel Laude , Panagiotis Patrinos

In this paper, we study the proximal incremental aggregated gradient(PIAG) algorithm for minimizing the sum of L-smooth nonconvex component functions and a proper closed convex function. By exploiting the L-smooth property and with the help…

Optimization and Control · Mathematics 2020-06-01 Wei Peng , Hui Zhang , Xiaoya Zhang

We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…

Optimization and Control · Mathematics 2024-04-12 Yutong Dai , Xiaoyi Qu , Daniel P. Robinson

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

The conditions of relative smoothness and relative strong convexity were recently introduced for the analysis of Bregman gradient methods for convex optimization. We introduce a generalized left-preconditioning method for gradient descent,…

Optimization and Control · Mathematics 2020-12-09 Chris J. Maddison , Daniel Paulin , Yee Whye Teh , Arnaud Doucet

We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…

Optimization and Control · Mathematics 2024-11-21 Hanyang Li , Ying Cui

In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…

Optimization and Control · Mathematics 2024-12-26 Hong Zhu

The proximal inertial gradient descent is efficient for the composite minimization and applicable for broad of machine learning problems. In this paper, we revisit the computational complexity of this algorithm and present other novel…

Optimization and Control · Mathematics 2019-07-19 Tao Sun , Linbo Qiao , Dongsheng Li

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

Optimization and Control · Mathematics 2025-07-16 Lei Wang , Le Bao , Xin Liu

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 develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…

Numerical Analysis · Mathematics 2016-05-13 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Optimization and Control · Mathematics 2019-05-27 Michael R. Metel , Akiko Takeda

This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…

Optimization and Control · Mathematics 2024-09-26 Gregorio M. Sempere , Welington de Oliveira , Johannes O. Royset