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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

This paper considers smooth convex optimization problems with many functional constraints. To solve this general class of problems we propose a new stochastic perturbed augmented Lagrangian method, called SGDPA, where a perturbation is…

Optimization and Control · Mathematics 2025-04-01 Nitesh Kumar Singh , Ion Necoara

We consider the convex-concave saddle point problem $\min_{\mathbf{x}}\max_{\mathbf{y}}\Phi(\mathbf{x},\mathbf{y})$, where the decision variables $\mathbf{x}$ and/or $\mathbf{y}$ subject to a multi-block structure and affine coupling…

Optimization and Control · Mathematics 2023-03-17 Junyu Zhang , Mengdi Wang , Mingyi Hong , Shuzhong Zhang

In this paper, we propose an inexact golden ratio primal-dual algorithm with linesearch step(IP-GRPDAL) for solving the saddle point problems, where two subproblems can be approximately solved by applying the notations of inexact extended…

Optimization and Control · Mathematics 2025-09-23 Changjie Fang , Jinxiu Liu , Jingtao Qiu , Shenglan Chen

In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…

Optimization and Control · Mathematics 2020-02-26 Julian Rasch , Antonin Chambolle

In this paper we propose a primal-dual dynamical approach to the minimization of a structured convex function consisting of a smooth term, a nonsmooth term, and the composition of another nonsmooth term with a linear continuous operator. In…

Optimization and Control · Mathematics 2020-08-03 Radu Ioan Bot , Ernö Robert Csetnek , Szilard Laszlo

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

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

This paper presents a simple primal dual method named DPD which is a flexible framework for a class of saddle point problem with or without strongly convex component. The presented method has linearized version named LDPD and exact version…

Optimization and Control · Mathematics 2019-07-16 Zhipeng Xie , Jianwen Shi

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

We propose two variants of the Primal Dual Hybrid Gradient (PDHG) algorithm for saddle point problems with block decomposable duals, hereafter called Multi-Timescale PDHG (MT-PDHG) and its accelerated variant (AMT-PDHG). Through novel…

Optimization and Control · Mathematics 2026-04-03 Junhui Zhang , Patrick Jaillet

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

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

Numerical Analysis · Mathematics 2025-06-16 Jianchao Bai , Linyuan Jia , Zheng Peng

In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems…

Optimization and Control · Mathematics 2024-10-16 Luke Fina , Christopher Petersen , Matthew Hale

We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap…

Optimization and Control · Mathematics 2024-10-29 Ewa Bednarczuk , The Hung Tran , Monika Syga

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

We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However,…

Optimization and Control · Mathematics 2017-03-09 Jialei Wang , Lin Xiao

Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we…

Optimization and Control · Mathematics 2023-09-12 Morteza Boroun , Zeinab Alizadeh , Afrooz Jalilzadeh

We present a parallelized primal-dual algorithm for solving constrained convex optimization problems. The algorithm is "block-based," in that vectors of primal and dual variables are partitioned into blocks, each of which is updated only by…

Optimization and Control · Mathematics 2020-09-01 Katherine Hendrickson , Matthew Hale

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