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In this paper, we develop a symmetric accelerated stochastic Alternating Direction Method of Multipliers (SAS-ADMM) for solving separable convex optimization problems with linear constraints. The objective function is the sum of a possibly…

Optimization and Control · Mathematics 2021-12-21 Jianchao Bai , Deren Han , Hao Sun , Hongchao Zhang

In this paper we propose a stochastic primal dual fixed point method (SPDFP) for solving the sum of two proper lower semi-continuous convex function and one of which is composite. The method is based on the primal dual fixed point method…

Optimization and Control · Mathematics 2020-04-21 YaNanZhu , XiaoqunZhang

Saddle point problems, ubiquitous in optimization, extend beyond game theory to diverse domains like power networks and reinforcement learning. This paper presents novel approaches to tackle saddle point problem, with a focus on…

Optimization and Control · Mathematics 2024-04-09 Anik Kumar Paul , Arun D Mahindrakar , Rachel K Kalaimani

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 develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

Optimization and Control · Mathematics 2021-04-20 Yuzixuan Zhu , Deyi Liu , Quoc Tran-Dinh

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 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

Classical primal-dual algorithms attempt to solve $\max_{\mu}\min_{x} \mathcal{L}(x,\mu)$ by alternatively minimizing over the primal variable $x$ through primal descent and maximizing the dual variable $\mu$ through dual ascent. However,…

Optimization and Control · Mathematics 2023-11-20 Kaizhao Sun , Andy Sun

This paper focuses on the distributed optimization of stochastic saddle point problems. The first part of the paper is devoted to lower bounds for the centralized and decentralized distributed methods for smooth (strongly) convex-(strongly)…

Machine Learning · Computer Science 2025-04-28 Aleksandr Beznosikov , Valentin Samokhin , Alexander Gasnikov

We consider stochastic convex optimization problems with affine constraints and develop several methods using either primal or dual approach to solve it. In the primal case, we use a special penalization technique to make the initial…

Optimization and Control · Mathematics 2020-11-13 Eduard Gorbunov , Darina Dvinskikh , Alexander Gasnikov

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

We provide an overview of primal-dual algorithms for nonsmooth and non-convex-concave saddle-point problems. This flows around a new analysis of such methods, using Bregman divergences to formulate simplified conditions for convergence.

Optimization and Control · Mathematics 2021-08-03 Tuomo Valkonen

The Primal-Dual hybrid gradient (PDHG) method is a powerful optimization scheme that breaks complex problems into simple sub-steps. Unfortunately, PDHG methods require the user to choose stepsize parameters, and the speed of convergence is…

Numerical Analysis · Mathematics 2015-03-25 Tom Goldstein , Min Li , Xiaoming Yuan , Ernie Esser , Richard Baraniuk

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

We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoothness assumptions, in which we allow for stochastic error in…

Optimization and Control · Mathematics 2021-12-23 Antonio Silveti-Falls , Cesare Molinari , Jalal Fadili

We consider a general class of nonsmooth optimal control problems with partial differential equation (PDE) constraints, which are very challenging due to its nonsmooth objective functionals and the resulting high-dimensional and…

Optimization and Control · Mathematics 2023-07-26 Yongcun Song , Xiaoming Yuan , Hangrui Yue

A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a…

Numerical Analysis · Computer Science 2013-01-01 Changzhi Wu , Chaojie Li , David Yang Gao

In this paper we consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods. We show that both of these algorithms admit a…

Optimization and Control · Mathematics 2019-09-06 Aryan Mokhtari , Asuman Ozdaglar , Sarath Pattathil

Primal-dual methods have a natural application in Safe Reinforcement Learning (SRL), posed as a constrained policy optimization problem. In practice however, applying primal-dual methods to SRL is challenging, due to the inter-dependency of…

Federated learning (FL) approaches for saddle point problems (SPP) have recently gained in popularity due to the critical role they play in machine learning (ML). Existing works mostly target smooth unconstrained objectives in Euclidean…

Machine Learning · Computer Science 2024-09-17 Site Bai , Brian Bullins