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We study preconditioned proximal point methods for a class of saddle point problems, where the preconditioner decouples the overall proximal point method into an alternating primal--dual method. This is akin to the Chambolle--Pock method or…

Optimization and Control · Mathematics 2020-02-13 Tuomo Valkonen

In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable…

Optimization and Control · Mathematics 2025-06-03 Hongjin He , Kai Wang , Jintao Yu

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…

Optimization and Control · Mathematics 2021-04-13 Renbo Zhao

This work proposes an Accelerated Primal-Dual Fixed-Point (APDFP) method that employs Nesterov type acceleration to solve composite problems of the form min f(x) + g(Bx), where g is nonsmooth and B is a linear operator. The APDFP features…

Optimization and Control · Mathematics 2025-11-04 Ya-Nan Zhu

The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work…

Optimization and Control · Mathematics 2018-11-21 Hung D. Nguyen , Thanh Long Vu , Konstantin Turitsyn , Jean-Jacques Slotine

In this paper, we adapt proximal incremental aggregated gradient methods to saddle point problems, which is motivated by decoupling linear transformations in regularized empirical risk minimization models. First, the Primal-Dual Proximal…

Optimization and Control · Mathematics 2019-11-14 Zhou Xianchen , Peng Wei , Wang Hongxia

We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent…

Optimization and Control · Mathematics 2024-10-04 Weijian Li , Xianlin Zeng , Lacra Pavel

In the present paper we propose a novel convergence analysis of the Alternating Direction Methods of Multipliers (ADMM), based on its equivalence with the overrelaxed Primal-Dual Hybrid Gradient (oPDHG) algorithm. We consider the smooth…

Optimization and Control · Mathematics 2017-01-19 Pauline Tan

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

In this paper, we propose a variance-reduced primal-dual algorithm with Bregman distance for solving convex-concave saddle-point problems with finite-sum structure and nonbilinear coupling function. This type of problems typically arises in…

Optimization and Control · Mathematics 2021-06-02 Erfan Yazdandoost Hamedani , Afrooz Jalilzadeh

This paper investigates two accelerated primal-dual mirror dynamical approaches for smooth and nonsmooth convex optimization problems with affine and closed, convex set constraints. In the smooth case, an accelerated primal-dual mirror…

Optimization and Control · Mathematics 2022-09-15 You Zhao , Xiaofeng Liao , Xing He , Chaojie Li

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…

Optimization and Control · Mathematics 2021-06-15 Vladislav Tominin , Yaroslav Tominin , Ekaterina Borodich , Dmitry Kovalev , Alexander Gasnikov , Pavel Dvurechensky

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

This paper is devoted to the design of efficient primal-dual algorithm (PDA) for solving convex optimization problems with known saddle-point structure. We present a new PDA with larger acceptable range of parameters and correction, which…

Optimization and Control · Mathematics 2019-12-04 Xiaokai Chang , Sanyang Liu

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 study a block-structured class of convex-concave saddle-point problems in which both the primal and dual variables admit natural separable decompositions. Motivated by large-scale applications where a full update on either side can be…

Optimization and Control · Mathematics 2026-05-19 Yiheng Xiao , Huikang Liu

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

The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…

Optimization and Control · Mathematics 2022-10-26 Egor Gladin , Ilya Kuruzov , Fedor Stonyakin , Dmitry Pasechnyuk , Mohammad Alkousa , Alexander Gasnikov

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

The primal-dual hybrid gradient (PDHG) method is one of the most popular algorithms for solving saddle point problems. However, when applying the PDHG method and its many variants to some real-world models commonly encountered in signal…

Optimization and Control · Mathematics 2025-06-10 Jintao Yu , Hongjin He