基于改进对偶分解的Optimization用于DSL动态频谱管理
Improved Dual Decomposition Based Optimization for DSL Dynamic Spectrum Management
摘要：
动态频谱管理（DSM）已被公认为是显著提高数字用户线（DSL）宽带接入网性能的关键技术。DSM的基本概念是协调多条DSL线路上的传输，以减轻它们之间串扰干扰的影响。针对DSM中的非凸最优化问题，已经提出了许多算法，几乎所有算法都依赖于标准的基于次梯度的对偶分解方法。然而，在实践中，这种方法经常被发现导致极其缓慢的收敛或甚至根本不收敛，原因之一是步长参数的非常困难的调整。在本文中，我们提出了一种新的改进的对偶分解方法的启发，在数学规划的最新进展。它使用了一个平滑技术的拉格朗日结合最佳梯度为基础的计划更新拉格朗日乘子。此外，最佳地选择步长参数，从而消除了对调谐策略的需要。通过这种方法，我们展示了如何收敛的当前国家的最先进的DSM算法的基础上迭代凸逼近（SCALE，CA-DSB）可以提高一个数量级。此外，我们将改进的对偶分解方法应用于其他DSM算法（OSB，ISB，ASB，（MS）-DSB，MIW），并提出进一步的改进，以获得快速和鲁棒的DSM算法。最后，我们证明了一些现实的多用户DSL场景的改进的对偶分解方法的有效性。
英文摘要：
Dynamic spectrum management (DSM) has been recognized as a key technology to significantly improve the performance of digital subscriber line (DSL) broadband access networks. The basic concept of DSM is to coordinate transmission over multiple DSL lines so as to mitigate the impact of crosstalk interference amongst them. Many algorithms have been proposed to tackle the nonconvex optimization problems appearing in DSM, almost all of them relying on a standard subgradient based dual decomposition approach. In practice however, this approach is often found to lead to extremely slow convergence or even no convergence at all, one of the reasons being the very difficult tuning of the stepsize parameters. In this paper we propose a novel improved dual decomposition approach inspired by recent advances in mathematical programming. It uses a smoothing technique for the Lagrangian combined with an optimal gradient based scheme for updating the Lagrange multipliers. The stepsize parameters are furthermore selected optimally removing the need for a tuning strategy. With this approach we show how the convergence of current state-of-the-art DSM algorithms based on iterative convex approximations (SCALE, CA-DSB) can be improved by one order of magnitude. Furthermore we apply the improved dual decomposition approach to other DSM algorithms (OSB, ISB, ASB, (MS)-DSB, MIW) and propose further improvements to obtain fast and robust DSM algorithms. Finally, we demonstrate the effectiveness of the improved dual decomposition approach for a number of realistic multi-user DSL scenarios.
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