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We propose a proximal variable smoothing algorithm for nonsmooth optimization problem with sum of three functions involving weakly convex composite function. The proposed algorithm is designed as a time-varying forward-backward splitting…

Optimization and Control · Mathematics 2025-04-29 Keita Kume , Isao Yamada

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

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…

Optimization and Control · Mathematics 2023-02-27 Laurent Condat , Daichi Kitahara , Andrés Contreras , Akira Hirabayashi

This paper is concerned with convex composite minimization problems in a Hilbert space. In these problems, the objective is the sum of two closed, proper, and convex functions where one is smooth and the other admits a computationally…

Optimization and Control · Mathematics 2020-02-19 Patrick R. Johnstone , Pierre Moulin

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…

Machine Learning · Statistics 2015-06-11 Atsushi Nitanda

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

Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…

Optimization and Control · Mathematics 2016-02-26 Patrick L. Combettes , Jean-Christophe Pesquet

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

Optimization and Control · Mathematics 2022-02-16 Meng Li , Paul Grigas , Alper Atamturk

The linear inverse problem emerges from various real-world applications such as Image deblurring, inpainting, etc., which are still thrust research areas for image quality improvement. In this paper, we have introduced a new algorithm…

Signal Processing · Electrical Eng. & Systems 2022-11-29 Avinash Kumar , Sujit Kumar Sahoo

In this paper we consider finite sum composite convex optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the…

Optimization and Control · Mathematics 2024-12-03 Nitesh Kumar Singh , Ion Necoara , Vyacheslav Kungurtsev

We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…

Optimization and Control · Mathematics 2018-11-07 Jingzhao Zhang , César A. Uribe , Aryan Mokhtari , Ali Jadbabaie

The ``fast iterative shrinkage-thresholding algorithm'', a.k.a. FISTA, is one of the most widely used algorithms in the literature. However, despite its optimal theoretical $O(1/k^2)$ convergence rate guarantee, oftentimes in practice its…

Optimization and Control · Mathematics 2018-07-12 Jingwei Liang , Carola-Bibiane Schönlieb

FISTA is a popular convex optimisation algorithm which is known to converge at an optimal rate whenever a minimiser is contained in a suitable Hilbert space. We propose a modified algorithm where each iteration is performed in a subset…

Optimization and Control · Mathematics 2022-10-06 Antonin Chambolle , Robert Tovey

The most popular first-order accelerated black-box methods for solving large-scale convex optimization problems are the Fast Gradient Method (FGM) and the Fast Iterative Shrinkage Thresholding Algorithm (FISTA). FGM requires that the…

Optimization and Control · Mathematics 2021-09-29 Mihai I. Florea , Sergiy A. Vorobyov

We consider iterative gradient-based optimization algorithms applied to functions that are smooth and strongly convex. The fastest globally convergent algorithm for this class of functions is the Triple Momentum (TM) method. We show that if…

Optimization and Control · Mathematics 2025-06-03 Bryan Van Scoy , Laurent Lessard

This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks. The local loss function in these problems contains both smooth and…

Optimization and Control · Mathematics 2023-03-07 Luyao Guo , Xinli Shi , Jinde Cao , Zihao Wang

In October 2025, research by Bo\c{t}, Fadili, and Nguyen, and by Jang and Ryu, led to the seminal result that Beck and Teboulle's FISTA converges weakly to a minimizer of the sum of two convex functions resolving a long-standing open…

Optimization and Control · Mathematics 2026-04-03 Sedi Bartz , Heinz H. Bauschke , Yuan Gao , Walaa M. Moursi

In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a…

Optimization and Control · Mathematics 2016-10-28 Jingwei Liang , Jalal Fadili , Gabriel Peyré

In this paper we develop a higher-order method for solving composite (non)convex minimization problems with smooth (non)convex functional constraints. At each iteration our method approximates the smooth part of the objective function and…

Optimization and Control · Mathematics 2025-03-04 Yassine Nabou , Ion Necoara

The accelerated composite optimization method FISTA (Beck, Teboulle 2009) is suboptimal by a constant factor, and we present a new method OptISTA that improves FISTA by a constant factor of 2. The performance estimation problem (PEP) has…

Optimization and Control · Mathematics 2026-02-17 Uijeong Jang , Shuvomoy Das Gupta , Ernest K. Ryu