scholarly journals A First-Order Primal-Dual Algorithm with Linesearch

2018 ◽  
Vol 28 (1) ◽  
pp. 411-432 ◽  
Author(s):  
Yura Malitsky ◽  
Thomas Pock
Keyword(s):  
Dual Algorithm ◽  
First Order ◽  
Primal Dual

An improved first-order primal-dual algorithm with a new correction step

2012 ◽  
Vol 57 (4) ◽  
pp. 1419-1428 ◽  
Author(s):  
Xingju Cai ◽  
Deren Han ◽  
Lingling Xu
Keyword(s):  
Dual Algorithm ◽  
First Order ◽  
Primal Dual ◽  
Correction Step

scholarly journals On the ergodic convergence rates of a first-order primal–dual algorithm

2015 ◽  
Vol 159 (1-2) ◽  
pp. 253-287 ◽  
Author(s):  
Antonin Chambolle ◽  
Thomas Pock
Keyword(s):  
Convergence Rates ◽  
Dual Algorithm ◽  
First Order ◽  
Primal Dual

scholarly journals A First-Order Stochastic Primal-Dual Algorithm with Correction Step

2017 ◽  
Vol 38 (5) ◽  
pp. 602-626 ◽  
Author(s):  
Lorenzo Rosasco ◽  
Silvia Villa ◽  
Bằng Công Vũ
Keyword(s):  
Dual Algorithm ◽  
First Order ◽  
Primal Dual ◽  
Correction Step

scholarly journals On the linear convergence of the general first order primal-dual algorithm

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kai Wang ◽  
Deren Han
Keyword(s):  
Linear Convergence ◽  
Analytical Framework ◽  
Dual Algorithm ◽  
Linear Rate ◽  
First Order ◽  
Convex Problems ◽  
Primal Dual ◽  
The One ◽  
Weaker Conditions ◽  
Special Case

<p style='text-indent:20px;'>In this paper, we consider the general first order primal-dual algorithm, which covers several recent popular algorithms such as the one proposed in [Chambolle, A. and Pock T., A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vis., 40 (2011) 120-145] as a special case. Under suitable conditions, we prove its global convergence and analyze its linear rate of convergence. As compared to the results in the literature, we derive the corresponding results for the general case and under weaker conditions. Furthermore, the global linear rate of the linearized primal-dual algorithm is established in the same analytical framework.</p>

scholarly journals An Implementable First-Order Primal-Dual Algorithm for Structured Convex Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Feng Ma ◽  
Mingfang Ni ◽  
Lei Zhu ◽  
Zhanke Yu
Keyword(s):  
Convex Optimization ◽  
Practical Interest ◽  
Principal Component ◽  
Objective Functions ◽  
Dual Algorithm ◽  
Proximal Point ◽  
Pursuit Problem ◽  
First Order ◽  
Structured Convex Optimization ◽  
Primal Dual

Many application problems of practical interest can be posed as structured convex optimization models. In this paper, we study a new first-order primaldual algorithm. The method can be easily implementable, provided that the resolvent operators of the component objective functions are simple to evaluate. We show that the proposed method can be interpreted as a proximal point algorithm with a customized metric proximal parameter. Convergence property is established under the analytic contraction framework. Finally, we verify the efficiency of the algorithm by solving the stable principal component pursuit problem.

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