On the implementation of ADMM with dynamically configurable parameter for the separable $$\ell _{1}/\ell _{2}$$ minimization

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED Optimization Letters Pub Date : 2024-03-26 DOI:10.1007/s11590-024-02106-z

Jun Wang, Qiang Ma

引用次数: 0

Abstract

In this paper, we propose a novel variant of the alternating direction method of multipliers (ADMM) approach for solving minimization of the rate of $\ell _{1}$ and $\ell _{2}$ norms for sparse recovery. We first transform the quotient of $\ell _{1}$ and $\ell _{2}$ norms into a new function of the separable variables using the least squares minimum norm solution of the linear system of equations. Subsequently, we employ the augmented Lagrangian function to formulate the corresponding ADMM method with a dynamically adjustable parameter. Additionally, each of its subproblems possesses a unique global minimum. Finally, we present some numerical experiments to demonstrate our results.

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关于针对可分离的 $$ell _{1}/\ell _{2}$ 最小化问题实现带动态可配置参数的 ADMM

在本文中，我们提出了一种交替方向乘法（ADMM）的新变体，用于解决稀疏恢复中的$\ell _{1}$和$\ell _{2}$规范率最小化问题。我们首先使用线性方程组的最小二乘最小规范解将 $\ell _{1}$ 和 $\ell _{2}$ 规范的商转换为可分离变量的新函数。随后，我们利用增强拉格朗日函数来制定相应的 ADMM 方法，并采用动态可调参数。此外，每个子问题都有一个唯一的全局最小值。最后，我们通过一些数值实验来证明我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.