Michaela Bailova, Jiri Bouchala, Petr Vodstrcil

Global Optimization Using Space Filling Curves

Číslo: 2/2017
Periodikum: Advances in Electrical and Electronic Engineering
DOI: 10.15598/aeee.v15i2.2303

Klíčová slova: Dimension reduction; global optimization; Hoelder continuity; Lipschitz continuity; space filling curves, Zmenšení rozměrů; Globální optimalizace; Hoelderova Kontinuita; Lipschitzova kontinuita; křivka vyplňující prostor.

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Anotace: The existence of space filling curves opens the way to reducing multivariate optimization problems to the minimization of univariate functions. In this paper, we analyze the Hoelder continuity of space filling curves and exploit this property in the solution of global optimization problems. Subsequently, an algorithm for minimizing univariate Hoelder continuous functions is presented and analyzed. It is shown that the algorithm computes the approximate minimum with the guaranteed precision. The algorithm is tested on some types of two-dimensional functions.