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

I haven't seen public domain software that addresses specifically univariate global optimizion with guarantee; but the interval codes referenced in the software section should handle this case without problems.

Global (and Local) Optimization
my home page (http://www.mat.univie.ac.at/~neum)

Arnold Neumaier (Arnold.Neumaier@univie.ac.at)