Univariate Global Optimization
The univariate case is simple because there is no curse of
dimensionality and a linear ordering of the arguments.
GLS, Global Line Search (by Arnold Neumaier)
contains a heuristic 1D global optimizer (in Matlab)
that works quite well in many cases.
But, as any global optimizion method based on function values only,
it cannot guarantee that the global optimum has been found.
To get results with some guarantee, one needs to use interval methods
(or other methods using semilocal or global information),
and a more or less unsurpassed treatment is given in
Global optimization using interval analysis - the one-dimensional case
J. Optim. Theory Appl. 29, 331-344 (1979)
I haven't seen public domain software that addresses specifically
univariate global optimizion with guarantee; but the
referenced in the software section should handle this case without
Global (and Local) Optimization
home page (http://www.mat.univie.ac.at/~neum)
Arnold Neumaier (Arnold.Neumaier@univie.ac.at)