Local Linear Convergence of a Primal-Dual Algorithm for the Augmented Convex Models

被引：0
作者：
Tao Sun
Roberto Barrio
Hao Jiang
Lizhi Cheng
机构：
[1] National University of Defense Technology,College of Science
[2] Universidad de Zaragoza,Departamento de Matemática Aplicada, IUMA and CoDy group
[3] National University of Defense Technology,College of Computer
[4] National University of Defense Technology,College of Science and The State Key Laboratory for High Performance Computation
来源：
Journal of Scientific Computing | 2016年 / 69卷
关键词：
Convex optimization; Primal-dual algorithm; Augmented convex model; Partial smoothness; Local linear convergence; 90C25; 65K10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Convex optimization has become an essential technique in many different disciplines. In this paper, we consider the primal-dual algorithm minimizing augmented models with linear constraints, where the objective function consists of two proper closed convex functions; one is the square of a norm and the other one is a gauge function being partly smooth relatively to an active manifold. Examples of this situation can be found in signal processing, optimization, statistics and machine learning literature. We present a unified framework to understand the local convergence behaviour of the primal-dual algorithm for these augmented models. This result explains some numerical results shown in the literature on local linear convergence of the algorithm.
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页码：1301 / 1315
页数：14
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