Implementing the Nelder-Mead simplex algorithm with adaptive parameters
Implementing the Nelder-Mead simplex algorithm with adaptive parameters
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DOI：
10.1007/s10589-010-9329-3
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发表时间：
2012-01-01
影响因子：
2.2
通讯作者：
Han, Lixing
中科院分区：
文献类型：
--
作者：
Gao, Fuchang;Han, Lixing
本文首先证明了当目标函数为一致凸时，Nelder-Mead单纯形算法的展开和收缩步具有下降性质。这个性质为为什么标准的Nelder-Mead算法在高维中变得低效提供了一些新的见解。然后，我们提出了一种Nelder-Mead方法的实现，其中膨胀、收缩和收缩参数取决于优化问题的维度。我们的数值实验表明，新的实现在高维问题上优于标准的Nelder-Mead方法。
In this paper, we first prove that the expansion and contraction steps of the Nelder-Mead simplex algorithm possess a descent property when the objective function is uniformly convex. This property provides some new insights on why the standard Nelder-Mead algorithm becomes inefficient in high dimensions. We then propose an implementation of the Nelder-Mead method in which the expansion, contraction, and shrink parameters depend on the dimension of the optimization problem. Our numerical experiments show that the new implementation outperforms the standard Nelder-Mead method for high dimensional problems.