二次耦合项不可分离凸极小化模型的优化iPADMM

Yumin Ma, T. Li, Yongzhong Song, Xingju Cai
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引用次数: 1

摘要

本文考虑了在许多实际应用中出现的二次耦合项的不可分凸极小化模型。我们使用乘法器的多数不定近端交替方向法(iPADMM)来求解这个模型。近端矩阵的不确定性使得我们实际解出的函数不再是每个子问题中原函数的极大化。在保证收敛性的同时,允许较大的步长加快收敛速度。对于该模型,我们分析了两种不同技术下的多数iPADMM的全局收敛性和非遍历意义下的次线性收敛率。数值实验说明了不定近端矩阵相对于正定或半定近端矩阵的优点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Majorized iPADMM for Nonseparable Convex Minimization Models with Quadratic Coupling Terms
In this paper, we consider nonseparable convex minimization models with quadratic coupling terms arised in many practical applications. We use a majorized indefinite proximal alternating direction method of multipliers (iPADMM) to solve this model. The indefiniteness of proximal matrices allows the function we actually solved to be no longer the majorization of the original function in each subproblem. While the convergence still can be guaranteed and larger stepsize is permitted which can speed up convergence. For this model, we analyze the global convergence of majorized iPADMM with two different techniques and the sublinear convergence rate in the nonergodic sense. Numerical experiments illustrate the advantages of the indefinite proximal matrices over the positive definite or the semi-definite proximal matrices.
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