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Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be…

Optimization and Control · Mathematics 2023-09-21 Bryan Van Scoy , John W. Simpson-Porco , Laurent Lessard

In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…

Optimization and Control · Mathematics 2022-08-31 Zhenyuan Zhu , Fan Chen , Junyu Zhang , Zaiwen Wen

We propose and analyze a general framework called nonlinear preconditioned primal-dual with projection for solving nonconvex-nonconcave and non-smooth saddle-point problems. The framework consists of two steps. The first is a nonlinear…

Optimization and Control · Mathematics 2024-01-11 Lu Zhang , Hongxia Wang , Hui Zhang

The saddle-point optimization problems have a lot of practical applications. This paper focuses on such non-smooth problems in decentralized case. This work contains generalization of recently proposed sliding for centralized problem.…

Optimization and Control · Mathematics 2024-01-01 Ilya Kuruzov , Alexander Rogozin , Demyan Yarmoshik , Alexander Gasnikov

This paper studies the primal-dual convergence and iteration-complexity of proximal bundle methods for solving nonsmooth problems with convex structures. More specifically, we develop a family of primal-dual proximal bundle methods for…

Optimization and Control · Mathematics 2025-09-26 Jiaming Liang

In Hilbert space, we propose a family of primal-dual dynamical system for affine constrained convex optimization problem. Several damping coefficients, time scaling coefficients, and perturbation terms are thus considered. By constructing…

Optimization and Control · Mathematics 2021-06-28 Xin He , Rong Hu , Ya-Ping Fang

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

Optimization and Control · Mathematics 2025-05-02 Michael Muehlebach , Michael I. Jordan

The primal-dual splitting algorithm (PDSA) by Chambolle and Pock is efficient for solving structured convex optimization problems. It adopts an extrapolation step and achieves convergence under certain step size condition. Chang and Yang…

Optimization and Control · Mathematics 2025-10-02 Xiaokai Chang , Junfeng Yang , Jianchao Bai , Jianxiong Cao

Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems…

Optimization and Control · Mathematics 2023-07-06 Alexander Engelmann , Gösta Stomberg , Timm Faulwasser

We consider (stochastic) convex-concave saddle point (SP) problems with high-dimensional decision variables, arising in various applications including machine learning problems. To contend with the challenges in computing full gradients, we…

Optimization and Control · Mathematics 2025-09-30 Erfan Yazdandoost Hamedani , Afrooz Jalilzadeh , Necdet Serhat Aybat

A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide…

Optimization and Control · Mathematics 2014-06-23 Patrick L. Combettes , Laurent Condat , Jean-Christophe Pesquet , Bang Cong Vu

Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of…

Machine Learning · Computer Science 2024-12-31 Shaogang Ren , Xiaoning Qian

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

This paper addresses a distributed convex optimization problem with a class of coupled constraints, which arise in a multi-agent system composed of multiple communities modeled by cliques. First, we propose a fully distributed…

Optimization and Control · Mathematics 2022-11-21 Yuto Watanabe , Kazunori Sakurama

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

In this paper, a centralized two-block separable optimization is considered for which a fully parallel primal-dual discrete-time algorithm with fixed step size is derived based on monotone operator splitting method. In this algorithm, the…

Optimization and Control · Mathematics 2020-09-30 S. Sh. Alaviani , A. G. Kelkar

We develop a novel randomised block coordinate primal-dual algorithm for a class of non-smooth ill-posed convex programs. Lying in the midway between the celebrated Chambolle-Pock primal-dual algorithm and Tseng's accelerated proximal…

Optimization and Control · Mathematics 2023-08-03 Mathias Staudigl , Paulin Jacquot

We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks. We show that the proposed method is optimal in terms of communication steps. Additionally, we propose a new analysis…

Optimization and Control · Mathematics 2019-11-28 Darina Dvinskikh , Eduard Gorbunov , Alexander Gasnikov , Pavel Dvurechensky , Cesar A. Uribe

We investigate the challenging problem of adversarial multi-armed bandits operating under time-varying constraints, a scenario motivated by numerous real-world applications. To address this complex setting, we propose a novel primal-dual…

Machine Learning · Computer Science 2026-01-28 Tareq Si Salem

In this paper, we develop a distributed algorithm for solving a class of distributed convex optimization problems where the local objective functions can be a general nonsmooth function, and all equalities and inequalities are network-wide…

Optimization and Control · Mathematics 2026-04-14 Yeong-Ung Kim , Hyo-Sung Ahn