# 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:

• Iteration 1: xc = 0.20, xt = -0.5
• Iteration 2: xc = 0.20, xt = 0.10
• Iteration 3: xc = 0.10, xt = 1.50
• Iteration 4: xc = 0.10, xt = -0.20
• Iteration 5: xc = 0.10, xt = 0.0
• Iteration 6: xc = 0.0, xt = -0.10
• Iteration 7: x* = 0.0
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
6/18/1998