Certain convergent search algorithms can be turned into chaotic
dynamic
systems by
renormalisation back to a standard region at each iteration. This allows
the
machinery of
ergodic theory to be used for a new probabilistic analysis of their behaviour.
Rates of
convergence can be redefined in terms of various entropies and ergodic
characteristics
(Kolmogorov and Rényi entropies and Lyapunov exponent). A special
class
of line-search
algorithms, which contains the Golden-Section algorithm, is studied in
detail. Their
associated dynamic systems exhibit a Markov partition property, from which
invariant
measures and ergodic characteristics can be computed. A case is made that
the Rényi entropy
is the most appropriate convergence criterion in this environment.