This short paper describes a simple subgradient-based techniques for deriving bounds on the optimal solution value when using the ADMM to solve convex optimization problems. The technique requires a bound on the magnitude of some optimal solution vector, but is otherwise completely general. Some computational examples using LASSO problems demonstrate that the technique can produce steadily converging bounds in situations in which standard Lagrangian bounds yield little or no useful information. A second set of experiments establishes a proof of concept indicating the potential practical usefulness of the bounding technique.

中文翻译：

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从ADMM导出解决方案值界限

这篇简短的文章介绍了一种简单的基于次梯度的技术，用于在使用ADMM解决凸优化问题时推导最佳解值的界限。该技术需要限制某个最佳解矢量的大小，但是在其他方面是完全通用的。一些使用LASSO问题的计算示例表明，在标准拉格朗日边界产生很少或没有有用信息的情况下，该技术可以产生稳定收敛的边界。第二组实验建立了概念验证，表明了边界技术的潜在实用性。