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首页> 外文期刊>Journal of Computational and Applied Mathematics >A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming
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A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming

机译：求解双块可分离凸编程的乘法器线性化交替方向方法的概括

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摘要

The linearized alternating direction method of multipliers (ADMM), with indefinite proximal regularization, has been proved to be efficient for solving separable convex optimization subject to linear constraints. In this paper, we present a generalization of linearized ADMM (G-LADMM) to solve two-block separable convex minimization model, which linearizes all the subproblems by choosing a proper positive-definite or indefinite proximal term and updates the Lagrangian multiplier twice in different ways. Furthermore, the proposed G-LADMM can be expressed as a proximal point algorithm (PPA), and all the subproblems are just to estimate the proximity operator of the function in the objective. We specify the domain of the proximal parameter and stepsizes to guarantee that G-LADMM is globally convergent. It turns out that our convergence domain of the proximal parameter and stepsizes is significantly larger than other convergence domains in the literature. The numerical experiments illustrate the improvements of the proposed G-LADMM to solve LASSO and image decomposition problems. (C) 2019 Elsevier B.V. All rights reserved.
机译：已经证明，具有无限期近端正则化的乘法器（ADMM）的线性化交替方向方法已经证明是为了求解经受线性约束的可分离凸优化的有效。在本文中，我们介绍了线性化的ADMM（G-LADMM）的概括来解决双块可分离的凸起最小化模型，通过选择适当的正面或无限期的近期术语并更新拉格朗日乘法器两次不同的子问题方法。此外，所提出的G-LADMM可以表示为近端点算法（PPA），并且所有子问题都只是为了估计目标中函数的接近算子。我们指定了近端参数的域，并介绍了保证G-Ladmm是全局收敛的。事实证明，我们的近端参数的收敛域和步骤的趋同域显着大于文献中的其他收敛域。数值实验说明了所提出的G-LADMM解决套索和图像分解问题的改进。 （c）2019 Elsevier B.v.保留所有权利。

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