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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

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

This article is devoted to one particular case of using universal accelerated proximal envelopes to obtain computationally efficient accelerated versions of methods used to solve various optimization problem setups. We propose a proximally…

Optimization and Control · Mathematics 2021-03-12 Dmitry Pasechnyuk , Vladislav Matyukhin

In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable convex function whose gradient satisfies a locally…

Optimization and Control · Mathematics 2023-06-29 Luis M. Briceno-Arias , Francisco José Silva , Xianjin Yang

We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. Even though these methods may originally require convexity to operate, the proposed…

Machine Learning · Statistics 2019-01-03 Courtney Paquette , Hongzhou Lin , Dmitriy Drusvyatskiy , Julien Mairal , Zaid Harchaoui

We introduce a new algorithm, extended regularized dual averaging (XRDA), for solving regularized stochastic optimization problems, which generalizes the regularized dual averaging (RDA) method. The main novelty of the method is that it…

Optimization and Control · Mathematics 2022-07-14 Jonathan W. Siegel , Jinchao Xu

We study the problem of minimizing a $m$-weakly convex and possibly nonsmooth function. Weak convexity provides a broad framework that subsumes convex, smooth, and many composite nonconvex functions. In this work, we propose a…

Optimization and Control · Mathematics 2025-09-04 Feng-Yi Liao , Yang Zheng

Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…

Optimization and Control · Mathematics 2023-11-20 Alessandro Scagliotti , Piero Colli Franzone

We present an accelerated gradient method for non-convex optimization problems with Lipschitz continuous first and second derivatives. The method requires time $O(\epsilon^{-7/4} \log(1/ \epsilon) )$ to find an $\epsilon$-stationary point,…

Optimization and Control · Mathematics 2017-02-03 Yair Carmon , John C. Duchi , Oliver Hinder , Aaron Sidford

In this paper, we study inexact high-order Tensor Methods for solving convex optimization problems with composite objective. At every step of such methods, we use approximate solution of the auxiliary problem, defined by the bound for the…

Optimization and Control · Mathematics 2020-12-23 Nikita Doikov , Yurii Nesterov

We propose a new stochastic coordinate descent method for minimizing the sum of convex functions each of which depends on a small number of coordinates only. Our method (APPROX) is simultaneously Accelerated, Parallel and PROXimal; this is…

Optimization and Control · Mathematics 2014-03-04 Olivier Fercoq , Peter Richtárik

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

A problem of great interest in optimization is to minimize a sum of two closed, proper, and convex functions where one is smooth and the other has a computationally inexpensive proximal operator. In this paper we analyze a family of…

Optimization and Control · Mathematics 2017-01-24 Patrick R. Johnstone , Pierre Moulin

Motivated by the limitation of analyzing oscillatory signals composed of multiple components with fast-varying instantaneous frequency, we approach the time-frequency analysis problem by optimization. Based on the proposed adaptive harmonic…

Numerical Analysis · Mathematics 2016-03-22 Matthieu Kowalski , Adrien Meynard , Hau-tieng Wu

Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods.…

Optimization and Control · Mathematics 2016-06-30 Yangyang Xu

We deal with monotone inclusion problems of the form $0\in Ax+Dx+N_C(x)$ in real Hilbert spaces, where $A$ is a maximally monotone operator, $D$ a cocoercive operator and $C$ the nonempty set of zeros of another cocoercive operator. We…

Functional Analysis · Mathematics 2013-06-04 Radu Ioan Bot , Ernö Robert Csetnek

This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…

Optimization and Control · Mathematics 2023-07-13 Maria-Luiza Vladarean , Nikita Doikov , Martin Jaggi , Nicolas Flammarion

Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given…

Optimization and Control · Mathematics 2020-08-04 Yuwen Chen , Antonio Orvieto , Aurelien Lucchi

We introduce a generic scheme for accelerating gradient-based optimization methods in the sense of Nesterov. The approach, called Catalyst, builds upon the inexact accelerated proximal point algorithm for minimizing a convex objective…

Machine Learning · Statistics 2018-06-20 Hongzhou Lin , Julien Mairal , Zaid Harchaoui

We propose a novel method, namely the accelerated mirror-prox (AMP) method, for computing the weak solutions of a class of deterministic and stochastic monotone variational inequalities (VI). The main idea of this algorithm is to…

Optimization and Control · Mathematics 2014-03-18 Yunmei Chen , Guanghui Lan , Yuyuan Ouyang