Lipschitz and Hölder global optimization using space-filling curves
The authors present and analyse four algorithms for the global optimisation of a scalar-valued function satisfying a Lipschitz condition that has \(n\) bound constrained arguments. The connecting idea is the usage of a space-filling Hilbert curve and a transformation of the multi-dimensional formulation to a univariate one. Two algorithms are based on a global approximation of the Hölder constant for the resulting univariate function. The other two algorithms exploit a so-called local tuning. Furthermore, both approaches can be combined with a so-called local improvement resulting in four different methods. The performance of the algorithms are analyzed for numerous test functions and \(n=2,3,4\). The results are presented and discussed in detail.
scientific article; zbMATH DE number 5704983
scientific article