We consider this second example to confirm that the first example was not an isolated anomaly and also to set the stage for two of the outstanding issues we propose to address.

Again we consider the sequence of proposed solutions using the
interpolation coupled with the optimization. We denote by
*x*_{c} the current best solution for
the "true" problem *f*(*x*) and by
*x _{t}* the trial solution proposed by the
approximation

- Iteration 1:
*x*_{c}= 0.20,*x*= -0.5_{t} - Iteration 2:
*x*_{c}= 0.20,*x*= 0.10_{t} - Iteration 3:
*x*_{c}= 0.10,*x*= 1.50_{t} - Iteration 4:
*x*_{c}= 0.10,*x*= -0.20_{t} - Iteration 5:
*x*_{c}= 0.10,*x*= 0.0_{t} - Iteration 6:
*x*_{c}= 0.0,*x*= -0.10_{t} - Iteration 7:
*x**= 0.0

At Iteration 7 we stop with a *confirmed* (local) minimizer of
*f* (at least to the resolution of the grid) at *x** =
0.0 and a decent approximation *a* to our objective
*f* on the interval [ -0.5, 1.5 ].

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