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In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators.…

Optimization and Control · Mathematics 2022-02-22 Francisco J. Aragón-Artacho , Radu I. Boţ , David Torregrosa-Belén

The Chambolle--Pock method is a versatile three-parameter algorithm designed to solve a broad class of composite convex optimization problems, which encompass two proper, lower semicontinuous, and convex functions, along with a linear…

Optimization and Control · Mathematics 2025-10-29 Sebastian Banert , Manu Upadhyaya , Pontus Giselsson

The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping…

Numerical Analysis · Mathematics 2015-06-03 Emil Y. Sidky , Jakob H. Jørgensen , Xiaochuan Pan

We develop block structure adapted primal-dual algorithms for non-convex non-smooth optimisation problems whose objectives can be written as compositions $G(x)+F(K(x))$ of non-smooth block-separable convex functions $G$ and $F$ with a…

Optimization and Control · Mathematics 2020-09-25 Stanislav Mazurenko , Jyrki Jauhiainen , Tuomo Valkonen

For the inclusion problem involving two maximal monotone operators, under the metric subregularity of the composite operator, we derive the linear convergence of the generalized proximal point algorithm and several splitting algorithms,…

Optimization and Control · Mathematics 2016-09-28 Li Shen , Shaohua Pan

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

In this paper, we propose a novel primal-dual proximal splitting algorithm (PD-PSA), named BALPA, for the composite optimization problem with equality constraints, where the loss function consists of a smooth term and a nonsmooth term…

Optimization and Control · Mathematics 2022-12-07 Luyao Guo , Jinde Cao , Xinli Shi , Shaofu Yang

In this paper, we propose a primal-dual splitting algorithm for a broad class of structured composite monotone inclusions that involve finitely many set-valued operators, compositions of set-valued operators with bounded linear operators,…

Optimization and Control · Mathematics 2026-05-14 Minh N. Dao , Hung M. Phan , Matthew K. Tam , Thang D. Truong

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 study the extension of the Chambolle--Pock primal-dual algorithm to nonsmooth optimization problems involving nonlinear operators between function spaces. Local convergence is shown under technical conditions including metric regularity…

Optimization and Control · Mathematics 2017-07-11 Christian Clason , Tuomo Valkonen

We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence…

Optimization and Control · Mathematics 2020-03-26 D. Russell Luke , Yura Malitsky

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 introduce the Boosted Double-proximal Subgradient Algorithm (BDSA), a novel splitting algorithm designed to address general structured nonsmooth and nonconvex mathematical programs expressed as sums and differences of…

Optimization and Control · Mathematics 2023-06-30 Francisco J. Aragón-Artacho , Pedro Pérez-Aros , David Torregrosa-Belén

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 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 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

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 demonstrate that difficult non-convex non-smooth optimization problems, such as Nash equilibrium problems and anisotropic as well as isotropic Potts segmentation model, can be written in terms of generalized conjugates of convex…

Optimization and Control · Mathematics 2021-08-27 Christian Clason , Stanislav Mazurenko , Tuomo Valkonen

In this paper we consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator. With the idea of coordinate descent, we design a…

Optimization and Control · Mathematics 2016-04-15 Meng Wen , Shigang Yue , Yuchao Tang , Jigen Peng

We generalize the well-known primal-dual algorithm proposed by Chambolle and Pock for saddle point problems, and improve the condition for ensuring its convergence. The improved convergence-guaranteeing condition is effective for the…

Optimization and Control · Mathematics 2021-12-02 Bingsheng He , Feng Ma , Shengjie Xu , Xiaoming Yuan