For Example, 3, show that the optimal value of x is x = 1. Data from
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For Example, 3, show that the optimal value of x is x∗ = 1.
Data from Example 3
and we will search for an optimal value of c in the closed interval [0, 3]. We choose a tolerance t = 0.2. We apply the Golden Section Search Method until an interval of uncertainty is less than 0.2. The results are summarized in Table 7.5.
Table 7.5
The length of the final interval is less than 0.2. We can estimate c∗ = (0.8115 + 0.9787) / 2 = 0.8951, with f (0.8951) = 2.5804. In the problem set, we ask you to show analytically that the optimal value for c is c = 8/ 9 ≈ 0.8889.
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Related Book For
A First Course In Mathematical Modeling
ISBN: 9781285050904
5th Edition
Authors: Frank R. Giordano, William P. Fox, Steven B. Horton
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