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We develop an inexact primal-dual first-order smoothing framework to solve a class of non-bilinear saddle point problems with primal strong convexity. Compared with existing methods, our framework yields a significant improvement over the…

Optimization and Control · Mathematics 2023-07-25 Le Thi Khanh Hien , Renbo Zhao , William B. Haskell

We consider the saddle point problem where the objective functions are abstract convex with respect to the class of quadratic functions. We propose primal-dual algorithms using the corresponding abstract proximal operator and investigate…

Optimization and Control · Mathematics 2026-01-13 Ewa Bednarczuk , The Hung Tran

We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…

Optimization and Control · Mathematics 2021-10-29 Quoc Tran-Dinh , Deyi Liu

The paper proposes a linesearch for a primal-dual method. Each iteration of the linesearch requires to update only the dual (or primal) variable. For many problems, in particular for regularized least squares, the linesearch does not…

Optimization and Control · Mathematics 2018-03-26 Yura Malitsky , Thomas Pock

We are interested in solving convex optimization problems with large numbers of constraints. Randomized algorithms, such as random constraint sampling, have been very successful in giving nearly optimal solutions to such problems. In this…

Optimization and Control · Mathematics 2016-11-29 William B. Haskell , Yu Pengqian

We study convex-concave saddle point problems with bilinear coupling, covering linearly constrained convex optimization and more general nonsmooth or constrained models via a proximable term in the dual objective. In linearly convergent…

Optimization and Control · Mathematics 2026-03-02 Meng Li , Paul Grigas

We consider strongly-convex-strongly-concave saddle point problems assuming we have access to unbiased stochastic estimates of the gradients. We propose a stochastic accelerated primal-dual (SAPD) algorithm and show that SAPD sequence,…

Optimization and Control · Mathematics 2024-09-04 Xuan Zhang , Necdet Serhat Aybat , Mert Gürbüzbalaban

By time discretization of a second-order primal-dual dynamical system with damping $\alpha/t$ where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal-dual algorithm for a…

Optimization and Control · Mathematics 2022-06-06 Xin He , Rong Hu , Ya-Ping Fang

This note is concerned with the problem of minimizing a separable, convex, composite (smooth and nonsmooth) function subject to linear constraints. We study a randomized block-coordinate interpretation of the Chambolle-Pock primal-dual…

Optimization and Control · Mathematics 2024-08-30 Olivier Bilenne

Convex optimization models find interesting applications, especially in signal/image processing and compressive sensing. We study some augmented convex models, which are perturbed by strongly convex functions, and propose a dual gradient…

Optimization and Control · Mathematics 2013-08-30 Hui Zhang , Lizhi Cheng , Wotao Yin

In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…

Optimization and Control · Mathematics 2024-11-28 Zhenwei Lin , Qi Deng

Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide…

Optimization and Control · Mathematics 2014-10-28 Jean-Christophe Pesquet , Audrey Repetti

We consider the problem of finding a saddle point for the convex-concave objective $\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)$, where $f$ is a convex function with locally Lipschitz gradient and $g$ is convex and possibly…

Optimization and Control · Mathematics 2021-10-29 Maria-Luiza Vladarean , Yura Malitsky , Volkan Cevher

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general…

Optimization and Control · Mathematics 2018-04-11 Antonin Chambolle , Matthias J. Ehrhardt , Peter Richtárik , Carola-Bibiane Schönlieb

Proximal splitting algorithms are well suited to solving large-scale nonsmooth optimization problems, in particular those arising in machine learning. We propose a new primal-dual algorithm, in which the dual update is randomized;…

Optimization and Control · Mathematics 2023-03-08 Laurent Condat , Peter Richtárik

In this paper, we propose a primal-dual algorithm with a novel momentum term using the partial gradients of the coupling function that can be viewed as a generalization of the method proposed by Chambolle and Pock in 2016 to solve saddle…

Optimization and Control · Mathematics 2020-10-22 Erfan Yazdandoost Hamedani , Necdet Serhat Aybat

In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish…

Optimization and Control · Mathematics 2017-01-25 Xiang Gao , Yangyang Xu , Shuzhong Zhang

In this work, we study two first-order primal-dual based algorithms, the Gradient Primal-Dual Algorithm (GPDA) and the Gradient Alternating Direction Method of Multipliers (GADMM), for solving a class of linearly constrained non-convex…

Optimization and Control · Mathematics 2018-02-27 Mingyi Hong , Jason D. Lee , Meisam Razaviyayn

This work studies multi-agent sharing optimization problems with the objective function being the sum of smooth local functions plus a convex (possibly non-smooth) function coupling all agents. This scenario arises in many machine learning…

Optimization and Control · Mathematics 2020-06-17 Sulaiman A. Alghunaim , Ming Yan , Ali H. Sayed

We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a…

Optimization and Control · Mathematics 2015-09-10 Yuchen Zhang , Lin Xiao