Global Convergence of Radial Basis Function Trust-Region Algorithms for Derivative-Free Optimization
Global Convergence of Radial Basis Function Trust-Region Algorithms for Derivative-Free Optimization
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DOI：
10.1137/120902434
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发表时间：
2013-05
期刊：
影响因子：
--
通讯作者：
Stefan M. Wild;C. Shoemaker
中科院分区：
文献类型：
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作者：
Stefan M. Wild;C. Shoemaker
我们分析了依赖于径向基函数插值模型的全局收敛的无导数信赖域算法。我们的结果扩展了Conn，Scheinberg和Vicente [SIAM J. Optim.，第20（2009）号决议，第10页。387--415]到具有非线性项的完全线性模型。我们描述了适合我们的分析的径向基函数的类型，从而显示了Wild，Regis和Shoemaker的ORBIT算法的一阶临界点的全局收敛[SIAM J. Sci.计算：第30（2008）号决议，第10页。3197- 3219]。使用ORBIT，我们提出了不同类型的径向基函数的一系列测试问题的数值结果。我们还展示了使用ORBIT在寻找当地最小值的计算昂贵的环境工程问题，涉及修复受污染的地下水。
We analyze globally convergent, derivative-free trust-region algorithms relying on radial basis function interpolation models. Our results extend the recent work of Conn, Scheinberg, and Vicente [SIAM J. Optim., 20 (2009), pp. 387--415] to fully linear models that have a nonlinear term. We characterize the types of radial basis functions that fit in our analysis and thus show global convergence to first-order critical points for the ORBIT algorithm of Wild, Regis, and Shoemaker [SIAM J. Sci. Comput., 30 (2008), pp. 3197--3219]. Using ORBIT, we present numerical results for different types of radial basis functions on a series of test problems. We also demonstrate the use of ORBIT in finding local minima on a computationally expensive environmental engineering problem involving remediation of contaminated groundwater.