Chapter 13: Divergent optimization algorithm and synthetic functions
When all else fails
Abstract
In this chapter, I discuss an unusual optimization algorithm. Why would anyone be interested in an algorithm that never converges to the solution you are looking for? This version of the fixed-point iteration, when approaching a zero or an optimum, emits a strong signal and allows you to detect a small interval likely to contain the solution: the zero or global optimum in question. It may approach the optimum quite well, but subsequent iterations do not lead to convergence: the algorithm eventually moves away from the optimum, or oscillates around the optimum without ever reaching it.
The fixed-point iteration [Wiki] is the mother of all optimization ...
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