反问题中的全局优化：克里金法与径向基函数的比较
Global optimization in inverse problems: A comparison of Kriging and radial basis functions
AI总结：
针对具有唯一解的非线性反问题，比较了基于径向基函数和克里金法的全局优化方法，并指出径向基函数算法的改进版本更具前景。
摘要：
我们研究具有唯一解的非线性反问题框架下的全局优化。这些问题通常是不适定的。目标函数的评估通常代价高昂，因为它涉及求解一个非平凡的正问题。这些问题的病态性需要正则化，而目标函数的高评估成本可以通过响应面技术来解决。Gutmann (2001) 提出的基于径向基函数的全局优化是一种具有正则化方面的响应面全局优化技术。另一方面，多篇文献提出使用基于克里金法的概率方法进行全局优化，作为非线性多模态目标函数的有效技术，从而提供了可信的停止规则 (Jones2001)。在比较了这两种概念后，我们认为对于非线性反问题，径向基函数算法的改进版本似乎是最有前景的方法。
英文摘要：
We study global optimization (GOP) in the framework of non-linear inverse problems with a unique solution. These problems are in general ill-posed. Evaluation of the objective function is often expensive, as it implies the solution of a non-trivial forward problem. The ill-posedness of these problems calls for regularization while the high evaluation cost of the objective function can be addressed with response surface techniques. The global optimization using Radial Basis Function (RBF) as presented by Gutmann (2001) is a response surface global optimization technique with regularizing aspects. Alternatively, several publications put forward global optimization using a probabilistic approach based upon Kriging as an efficient technique for non-linear multi modal objective functions, thereby providing a credible stopping rule (Jones2001). After comparing both concepts, we argue that in case of non-linear inverse problems an adaptation of the RBF algorithm seems to be the most promising approach.
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