Let's reconsider the second example. When the optimization finishes at Iteration 7, we have a confirmed minimizer at 0.0 and our cubic spline approximation is quite accurate in the neighborhood of the minimizer [ -0.2, 0.2 ]. But the approximation is not particularly good in the region [ 0.833, 1.5 ]; in fact, the approximation a suggests that there is another local minimizer of the objective f in this region when none exists.
So let's perturb our function f and introduce a new basin that contains a global minimizer in the region [ 0.833, 1.5 ] and see what happens.
Optimization Using Approximations:
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