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Related papers: Chambolle-Pock's Primal-Dual Method with Mismatche…

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In this paper, we study saddle point (SP) problems, focusing on convex-concave optimization involving functions that satisfy either two-sided quadratic functional growth (QFG) or two-sided quadratic gradient growth (QGG)--novel conditions…

Optimization and Control · Mathematics 2025-10-15 Cody Melcher , Afrooz Jalilzadeh , Erfan Yazdandoost Hamedani

In this paper, we propose two novel non-stationary first-order primal-dual algorithms to solve nonsmooth composite convex optimization problems. Unlike existing primal-dual schemes where the parameters are often fixed, our methods use…

Optimization and Control · Mathematics 2020-07-13 Quoc Tran-Dinh , Yuzixuan Zhu

In this article, we propose a preconditioned Halpern iteration with adaptive anchoring parameters (PHA) by integrating a preconditioner and Halpern iteration with adaptive anchoring parameters. Then we establish the strong convergence and…

Optimization and Control · Mathematics 2026-02-13 Fangbing Lv , Qiao-Li Dong

The primal-dual algorithm recently proposed by Chambolle & Pock (abbreviated as CPA) for structured convex optimization is very efficient and popular. It was shown by Chambolle & Pock in \cite{CP11} and also by Shefi & Teboulle in…

Optimization and Control · Mathematics 2014-09-11 Raymond H. Chan , Shiqian Ma , Junfeng Yang

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 study and develop (stochastic) primal--dual block-coordinate descent methods for convex problems based on the method due to Chambolle and Pock. Our methods have known convergence rates for the iterates and the ergodic gap: $O(1/N^2)$ if…

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

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

Primal-dual methods for solving convex optimization problems with functional constraints often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at a sublinear rate. Then, after a certain point, the method…

Optimization and Control · Mathematics 2026-02-12 Mateo Díaz , Pedro Izquierdo Lehmann , Haihao Lu , Jinwen Yang

In this paper we study the convex-concave saddle-point problem $\min_x \max_y f(x) + y^T \mathbf{A} x - g(y)$, where $f(x)$ and $g(y)$ are smooth and convex functions. We propose an Accelerated Primal-Dual Gradient Method (APDG) for solving…

Optimization and Control · Mathematics 2022-03-10 Dmitry Kovalev , Alexander Gasnikov , Peter Richtárik

In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of…

Optimization and Control · Mathematics 2015-02-10 Mariette Annergren , Sina Khoshfetrat Pakazad , Anders Hansson , Bo Wahlberg

We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this efficiency through not solving the PDE or its linearisation on each iteration of the optimization…

Optimization and Control · Mathematics 2024-06-11 Bjørn Jensen , Tuomo Valkonen

We consider a network of agents, each with its own private cost consisting of the sum of two possibly nonsmooth convex functions, one of which is composed with a linear operator. At every iteration each agent performs local calculations and…

Optimization and Control · Mathematics 2017-03-14 Puya Latafat , Lorenzo Stella , Panagiotis Patrinos

In the paper, we develop a composite version of Mirror Prox algorithm for solving convex-concave saddle point problems and monotone variational inequalities of special structure, allowing to cover saddle point/variational analogies of what…

Optimization and Control · Mathematics 2014-05-23 Niao He , Anatoli Juditsky , Arkadi Nemirovski

We consider a primal-dual algorithm for minimizing $f(x)+h\square l(Ax)$ with Fr\'echet differentiable $f$ and $l^*$. This primal-dual algorithm has two names in literature: Primal-Dual Fixed-Point algorithm based on the Proximity Operator…

Optimization and Control · Mathematics 2021-02-02 Zhi Li , Ming Yan

We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…

Optimization and Control · Mathematics 2025-07-10 Ronak Mehta , Jelena Diakonikolas , Zaid Harchaoui

We introduce and analyze a continuous primal-dual dynamical system in the context of the minimization problem $f(x)+g(Ax)$, where $f$ and $g$ are convex functions and $A$ is a linear operator. In this setting, the trajectories of the…

Optimization and Control · Mathematics 2025-06-03 Vassilis Apidopoulos , Cesare Molinari , Juan Peypouquet , Silvia Villa

We present a novel accelerated primal-dual (APD) method for solving a class of deterministic and stochastic saddle point problems (SPP). The basic idea of this algorithm is to incorporate a multi-step acceleration scheme into the…

Optimization and Control · Mathematics 2013-09-24 Yunmei Chen , Guanghui Lan , Yuyuan Ouyang

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

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 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