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The ADMM Algorithm for Distributed Quadratic Problems: Parameter Selection and Constraint Preconditioning

机译:分布式二次问题的ADMM算法:参数选择和约束预处理

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This paper presents optimal parameter selection and preconditioning of the alternating direction method of multipliers (ADMM) algorithm for a class of distributed quadratic problems, which can be formulated as equality-constrained quadratic programming problems. The parameter selection focuses on the ADMM step-size and relaxation parameter, while the preconditioning corresponds to selecting the edge weights of the underlying communication graph. We optimize these parameters to yield the smallest convergence factor of the iterates. Explicit expressions are derived for the step-size and relaxation parameter, as well as for the corresponding convergence factor. Numerical simulations justify our results and highlight the benefits of optimal parameter selection and preconditioning for the ADMM algorithm.
机译:针对一类分布二次问题,提出了乘数交替方向法(ADMM)算法的最优参数选择和预处理,可以将其表示为等式约束二次规划问题。参数选择集中在ADMM步长和松弛参数上,而预处理对应于选择基础通信图的边缘权重。我们优化这些参数以产生迭代的最小收敛因子。为步长和松弛参数以及相应的收敛因子导出了明确的表达式。数值模拟证明了我们的结果的正确性,并强调了ADMM算法的最佳参数选择和预处理的好处。

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