Journal ArticleDOI
A modification of the Arrow-Hurwicz method for search of saddle points
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This article is published in Mathematical Notes.The article was published on 1980-11-01. It has received 250 citations till now. The article focuses on the topics: Monkey saddle & Saddle point.read more
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A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Antonin Chambolle,Thomas Pock +1 more
TL;DR: A first-order primal-dual algorithm for non-smooth convex optimization problems with known saddle-point structure can achieve O(1/N2) convergence on problems, where the primal or the dual objective is uniformly convex, and it can show linear convergence, i.e. O(ωN) for some ω∈(0,1), on smooth problems.
Journal ArticleDOI
A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science
TL;DR: This work generalizes the primal-dual hybrid gradient (PDHG) algorithm to a broader class of convex optimization problems, and surveys several closely related methods and explains the connections to PDHG.
An introduction to Total Variation for Image Analysis
TL;DR: Fornasier and Romlau as mentioned in this paper discuss various theoretical and practical topics related to total variation-based image reconstruction, focusing first on some theoretical results on functions which minimize the total variation, and in a second part, describe a few standard and less standard algorithms to minimize the overall variation in a finite-differences setting.
Proceedings ArticleDOI
An algorithm for minimizing the Mumford-Shah functional
TL;DR: The contribution of this paper is to propose an algorithm which allows to minimize a convex relaxation of the Mumford-Shah functional obtained by functional lifting, an efficient primal-dual projection algorithm for which it is proved convergence.
Journal ArticleDOI
Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective
Bingsheng He,Xiaoming Yuan +1 more
TL;DR: This paper shows that these new primal-dual methods proposed for solving a saddle-point problem are of the contraction type: the iterative sequences generated by these new methods are contractive with respect to the solution set of the saddle- point problem and the global convergence can be obtained within the analytic framework of contraction-type methods.
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