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首页> 外文会议>Conference on Optical Design and Engineering; Sep 30-Oct 3, 2003; St.Etienne, France >Topography of the merit function landscape in optical system design
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Topography of the merit function landscape in optical system design

机译：光学系统设计中功能函数景观的地形

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摘要

We have shown recently that, when certain quite general conditions are satisfied, the set of local minima in the optical merit function space forms a network where they are all connected through optimization paths generated from saddle points having a Morse index of 1. A new global optimization method, that makes use of this linking network to systematically detect all minima, is presented. The central component of this new method, the algorithm for saddle point detection, is described in detail and we show that the initialization of this algorithm has a significant impact on the performance. For a simple global optimization search (Cooke triplet) several representation forms of the network of the corresponding set of local minima are presented. These representations, which can be visualized in two dimensions, are independent of the dimensionality of the design space so that they can provide insight into the topography of merit function landscapes of arbitrary dimensionality.
机译：最近我们表明，当满足某些相当普遍的条件时，光学优值函数空间中的局部极小值集合形成一个网络，在该网络中，它们全部通过莫尔斯系数为1的鞍点生成的优化路径进行连接。提出了一种优化方法，该方法利用此链接网络系统地检测所有最小值。详细介绍了这种新方法的核心部分，即鞍点检测算法，并且我们证明了该算法的初始化对性能有重大影响。对于简单的全局优化搜索（Cooke三元组），给出了局部极小值的相应集合的网络的几种表示形式。这些表示形式可以在两个维度上可视化，而与设计空间的维度无关，因此它们可以洞察任意维度的价值函数景观的拓扑。

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