Topic
Rate of convergence
About: Rate of convergence is a research topic. Over the lifetime, 31257 publications have been published within this topic receiving 795334 citations. The topic is also known as: convergence rate.
Papers published on a yearly basis
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TL;DR: It is shown that if this computation is replaced by an approximate solution produced by an arbitrary iterative method, then with relatively modest requirements on the accuracy of the approximate solution, the resulting inexact Uzawa algorithm is convergent, with a convergence rate close to that of the exact algorithm.
Abstract: Variants of the Uzawa algorithm for solving symmetric indefinite linear systems are developed and analyzed. Each step of this algorithm requires the solution of a symmetric positive- definite system of linear equations. It is shown that if this computation is replaced by an approximate solution produced by an arbitrary iterative method, then with relatively modest requirements on the accuracy of the approximate solution, the resulting inexact Uzawa algorithm is convergent, with a convergence rate close to that of the exact algorithm. In addition, it is shown that preconditioning can be used to improve performance. The analysis is illustrated and supplemented using several examples derived from mixed finite element discretization of the Stokes equations.
487 citations
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TL;DR: This paper finds the optimal algorithm parameters that minimize the convergence factor of the ADMM iterates in the context of ℓ2-regularized minimization and constrained quadratic programming.
Abstract: The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the impact of the algorithm parameters on the convergence times of the method is still lacking. In this paper we find the optimal algorithm parameters that minimize the convergence factor of the ADMM iterates in the context of l2-regularized minimization and constrained quadratic programming. Numerical examples show that our parameter selection rules significantly outperform existing alternatives in the literature.
484 citations
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TL;DR: An alternative convergence proof of a proximal-like minimization algorithm using Bregman functions, recently proposed by Censor and Zenios, is presented and allows the establishment of a global convergence rate of the algorithm expressed in terms of function values.
Abstract: An alternative convergence proof of a proximal-like minimization algorithm using Bregman functions, recently proposed by Censor and Zenios, is presented. The analysis allows the establishment of a global convergence rate of the algorithm expressed in terms of function values.
481 citations
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TL;DR: A general approach to analyzing the convergence and the rate of convergence of feasible descent methods that does not require any nondegeneracy assumption on the problem is surveyed and extended.
Abstract: We survey and extend a general approach to analyzing the convergence and the rate of convergence of feasible descent methods that does not require any nondegeneracy assumption on the problem. This approach is based on a certain error bound for estimating the distance to the solution set and is applicable to a broad class of methods.
477 citations
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TL;DR: The proposed methodology may allow the upgrading of an existing evaluation to incorporate the genomic information when the information attributable to genomics can be expressed as modifications to the numerator relationship matrix.
475 citations