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Convergence rate analysis of primal-dual splitting schemes [article]

Damek Davis
2015 arXiv   pre-print
Finally, we apply our results to a large class of primal-dual algorithms that are a special case of our scheme and deduce their convergence rates.  ...  Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces.  ...  The following is our main tool to bound the pre-primal-dual gap. Proposition 2.6 (Upper fundamental inequality for primal dual schemes).  ... 
arXiv:1408.4419v3 fatcat:ghgmlcblvzav5cyojquaywx4vm

A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization [article]

Quoc Tran-Dinh, Olivier Fercoq, Volkan Cevher
2018 arXiv   pre-print
We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications.  ...  Our analysis relies on a novel combination of three classic ideas applied to the primal-dual gap function: smoothing, acceleration, and homotopy.  ...  The primal-dual update scheme.  ... 
arXiv:1507.06243v7 fatcat:b4mzxgyoubb3th2z736bi3nske

Generalised primal-dual grids for unstructured co-volume schemes

Darren Engwirda
2018 Journal of Computational Physics  
This new framework aims to extend the conventional Delaunay-Voronoi primal-dual structure; seeking to assemble generalised orthogonal tessellations with enhanced geometric quality.  ...  The performance of this new method is tested experimentally, with a range of complex, multi-resolution primal-dual grids generated for various coastal and regional ocean modelling applications.  ...  ; seeking to generate optimal primal-dual pairs appropriate for a co-volume type discretisation scheme.  ... 
doi:10.1016/j.jcp.2018.07.025 fatcat:svlmeafbmngnzcgibz3cx6vadq

Convergence Rate Analysis of Primal-Dual Splitting Schemes

Damek Davis
2015 SIAM Journal on Optimization  
Finally, we apply our results to a large class of primal-dual algorithms that are a special case of our scheme and deduce their convergence rates.  ...  Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces.  ...  The following is our main tool to bound the pre-primal-dual gap. Proposition 2.6 (Upper fundamental inequality for primal dual schemes).  ... 
doi:10.1137/151003076 fatcat:khaaw5wmmrfbznijgqvghpzogy

Stochastic Primal-Dual Proximal ExtraGradient descent for compositely regularized optimization

Tianyi Lin, Linbo Qiao, Teng Zhang, Jiashi Feng, Bofeng Zhang
2018 Neurocomputing  
To address these issues, we propose a stochastic variant of extra-gradient type methods, namely Stochastic Primal-Dual Proximal ExtraGradient descent (SPDPEG), and analyze its convergence property for  ...  The SPDPEG algorithm is based on the primal-dual update scheme where (z, x) is primal variable and λ is a dual variable, and can be seen as an inexact augmented Lagrangian method.  ...  Our contribution: We propose a novel Stochastic Primal-Dual Proximal Extra-Gradient Descent (SPDPEG). SPDPEG is efficient in solving large-scale problems with composite and nonsmooth regularizations.  ... 
doi:10.1016/j.neucom.2017.07.066 fatcat:vupm42zhv5g4to2jwsnbzjsrf4

Stochastic primal dual fixed point method for composite optimization [article]

YaNanZhu, XiaoqunZhang
2020 arXiv   pre-print
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 (PDFP) proposed in [7] that does not require subproblem solving.  ...  In this paper, we propose the stochastic primal dual fixed-point algorithm for solving the problem considered in (1.1).  ... 
arXiv:2004.09071v1 fatcat:raasmqn3ffhd3lh2x3f6bfmoni

An inertial primal-dual fixed point algorithm for composite optimization problems [article]

Meng Wen, Yu-Chao Tang, Jigen Peng
2016 arXiv   pre-print
We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1).  ...  This work brings together and notably extends several classical splitting schemes, like the primaldual method proposed by Chambolle and Pock, and the recent proximity algorithms of Charles A. et al designed  ...  Algorithm 1 An inertial primal-dual fixed point algorithm(IPDFP).  ... 
arXiv:1604.05299v1 fatcat:4tftn5mia5bpbd2nzo42zvg2wy

Two Modified Schemes for the Primal Dual Fixed Point Method

Ya-Nan Zhu & Xiaoqun Zhang
2021 CSIAM Transactions on Applied Mathematics  
The primal dual fixed point (PDFP) proposed in [7] was designed to solve convex composite optimization problems in imaging and data sciences.  ...  In this paper we study two modified schemes in order to accelerate its performance.  ...  primal dual fixed point method (PDFP) [7] .  ... 
doi:10.4208/csiam-am.2020-0042 fatcat:jsnmwpjsfnf4tjpu47dv6kjxqy

Stochastic Primal-Dual Coordinate Method with Large Step Size for Composite Optimization with Composite Cone-constraints [article]

Daoli Zhu, Lei Zhao
2019 arXiv   pre-print
We introduce a stochastic coordinate extension of the first-order primal-dual method studied by Cohen and Zhu (1984) and Zhao and Zhu (2018) to solve Composite Optimization with Composite Cone-constraints  ...  The linearization and Bregman-like function (core function) to that randomly selected block allow us to get simple parallel primal-dual decomposition for COCC.  ...  STOCHASTIC PRIMAL-DUAL COORDINATE METHOD In this section, we propose a stochastic primal-dual coordinate descent algorithm to solve (P).  ... 
arXiv:1905.01020v1 fatcat:qfj4g5nvcffjfbwvprqgigxiai

A second order primal-dual method for nonsmooth convex composite optimization [article]

Neil K. Dhingra, Sei Zhen Khong, Mihailo R. Jovanović
2020 arXiv   pre-print
Furthermore, we develop a globally convergent customized algorithm that utilizes the primal-dual augmented Lagrangian as a merit function.  ...  We develop a second order primal-dual method for optimization problems in which the objective function is given by the sum of a strongly convex twice differentiable term and a possibly nondifferentiable  ...  We develop a second order primal-dual algorithm for nonsmooth composite optimization by leveraging these advances.  ... 
arXiv:1709.01610v2 fatcat:c5ghicwpjrejllihvir7zr7w7i

A New Randomized Primal-Dual Algorithm for Convex Optimization with Optimal Last Iterate Rates [article]

Quoc Tran-Dinh, Deyi Liu
2021 arXiv   pre-print
Our convergence rates are obtained through three criteria: primal objective residual and primal feasibility violation, dual objective residual, and primal-dual expected gap.  ...  We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings  ...  Primal-dual expected gap.  ... 
arXiv:2003.01322v3 fatcat:5falgb6kyndpvmfzcxhsq2zlha

Accelerated first-order primal-dual proximal methods for linearly constrained composite convex programming [article]

Yangyang Xu
2016 arXiv   pre-print
In addition to the composite convexity, it further assumes two-block structure on the objective.  ...  This paper proposes two accelerated methods towards solving structured linearly constrained convex programming, for which we assume composite convex objective.  ...  This assumption is also made in several accelerated primal-dual methods for solving bilinear saddle-point problems, e.g., [3] [4] [5] 16] .  ... 
arXiv:1606.09155v1 fatcat:ygynyd5ztzcoxbjggrp7e5ee44

A stochastic coordinate descent inertial primal-dual algorithm for large-scale composite optimization [article]

Meng Wen, Yu-Chao Tang, Jigen Peng
2016 arXiv   pre-print
We consider an inertial primal-dual algorithm to compute the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator.  ...  Then the convergence of stochastic coordinate descent inertial primal-dual splitting algorithm is derived by applying the inertial version of the randomized Krasnosel'skii-Mann iterations to the composition  ...  This iteration, which is referred to as a primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms.  ... 
arXiv:1604.04845v1 fatcat:2xb3dt44prb67btvjbseh5j6bm

A stochastic primal-dual algorithm for distributed asynchronous composite optimization

Pascal Bianchi, Walid Hachem, Franck Iutzeler
2014 2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP)  
In this paper, we combine recent results on primal-dual optimization and coordinate descent to propose an asynchronous distributed algorithm for composite optimization.  ...  Consider a network where each agent has a private composite function (e.g. the sum of a smooth and a non-smooth function).  ...  While the distributed gradient and ADMM are respectively primal and dual methods, in this paper, we investigate a primal-dual algorithm for distributed composite optimization.  ... 
doi:10.1109/globalsip.2014.7032215 dblp:conf/globalsip/BianchiHI14 fatcat:rjerycz7zbfp5hamgyuo3tcgpu

A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization

Quoc Tran-Dinh, Olivier Fercoq, Volkan Cevher
2018 SIAM Journal on Optimization  
Our analysis relies on a novel combination of three classic ideas applied to the primal-dual gap function: smoothing, acceleration, and homotopy.  ...  We propose a new and low per-iteration complexity first-order primal-dual optimization framework for a convex optimization template with broad applications.  ...  The primal-dual update scheme.  ... 
doi:10.1137/16m1093094 fatcat:ermqxjrgwbek5f7dlzicbddffy
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