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Discussion of Second Example Revisited


Not too suprisingly--since that was the purpose of the construction--we see the same sequence of iterates that we saw for the second example:

The optimization correctly identifies a local minimizer of the objective f--which is all that the analysis guarantees. However, because of the poor quality of the approximation a in the region [ 0.833, 1.5 ], the optimization mistakenly assumes that the global solution is at 0.0 rather than (near) 1.3.

The question then becomes, how to balance our desire to find a confirmed minimizer with our desire to "know" enough about the function to avoid missing a potentially better solution simply because the approximation may not be sufficiently good to predict a better solution?

Next: An Alternate Outcome: Previous: Second Example Revisited:

Virginia Torczon