An augmented Lagrangian relaxation for analytical target cascading using the alternating direction method of multipliers
An augmented Lagrangian relaxation for analytical target cascading using the alternating direction method of multipliers
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DOI：
10.1007/s00158-005-0579-0
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发表时间：
2006-02
影响因子：
3.9
通讯作者：
S. Tosserams;L. Etman;P. Papalambros;J. Rooda
中科院分区：
文献类型：
--
作者：
S. Tosserams;L. Etman;P. Papalambros;J. Rooda
分析目标级联是一种分层、多级系统设计优化的方法。采用系统一致性约束的二次惩罚松弛来保证子问题的可行性。典型的嵌套解决方案策略由内部循环和外部循环组成。在内环中，采用固定惩罚权迭代求解耦合子问题。在内环收敛后，外环更新惩罚权值。本文提出了一种增广拉格朗日松弛法，它减少了内环中子问题的病态所带来的计算开销。采用乘法器交替方向法在单次内循环迭代后更新惩罚参数，使子问题只需要求解一次。四个实例的实验表明，计算成本降低了10到1000个数量级。
Analytical target cascading is a method for design optimization of hierarchical, multilevel systems. A quadratic penalty relaxation of the system consistency constraints is used to ensure subproblem feasibility. A typical nested solution strategy consists of inner and outer loops. In the inner loop, the coupled subproblems are solved iteratively with fixed penalty weights. After convergence of the inner loop, the outer loop updates the penalty weights. The article presents an augmented Lagrangian relaxation that reduces the computational cost associated with ill-conditioning of subproblems in the inner loop. The alternating direction method of multipliers is used to update penalty parameters after a single inner loop iteration, so that subproblems need to be solved only once. Experiments with four examples show that computational costs are decreased by orders of magnitude ranging between 10 and 1000.