Example:Nelder-Mead Method

本文介绍了一种迭代算法,该算法通过不断缩小三角形序列来逼近解决方案点(3,2),并最终达到最佳顶点B=(2.99996456,1.99983839),函数值f(B)=−6.99999998,接近理论值f(3,2)=−7。文章提供了迭代过程中三角形顶点的函数值,并讨论了由于函数在最小值附近变得平坦而导致迭代提前终止的原因。

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The process continues and generates a sequence of triangles that converges down on thesolution point (3, 2) (see Figure 8.10). Table 8.6 gives the function values at vertices of thetriangle for several steps in the iteration. A computer implementation of the algorithm continueduntil the thirty-third step, where the best vertex was B = (2.99996456, 1.99983839)and f (B) = −6.99999998. These values are approximations to f (3, 2) = −7 found inExample 8.5. The reason that the iteration quit before (3, 2) was obtained is that the functionis flat near the minimum. The function values f (B), f (G), and f (W) were checked(see Table 8.6) and found to be the same (this is an example of round-off error), and thealgorithm was terminated





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