Global minimization algorithms for Holder functions

This paper deals with the one-dimensional global optimization
problem where the objective function satisfies H\"{o}lder
condition over a closed interval. A direct extension of the
popular Piyavskii method proposed for Lipschitz functions to
H\"{o}lder optimization requires an a priori estimate of the
H\"{o}lder constant and solution to an equation of degree $N$ at
each iteration. In this paper a new scheme is introduced. Three
algorithms are proposed for solving one-dimensional H\"{o}lder
global optimization problems. All of them work without solving
equations of degree $N$. The case (very often arising in
applications) when H\"{o}lder constant is not given a priori is
considered. It is shown that local information about the
objective function used inside the global procedure can
accelerate the search significantly. Numerical experiments show
quite promising performance of the new algorithms.