In this paper the global optimization problem where the objective function is multiextremal and satisfying the Lipschitz condition over a hyperinterval is considered. An algorithm that uses Peano-type space-filling curves to reduce the original Lipschitz multi-dimensional problem to a univariate one satisfying the Hölder condition is proposed. The algorithm at each iteration applies a new geometric technique working with a number of possible Hölder constants chosen from a set of values varying from zero to infinity showing so that ideas introduced in a popular DIRECT method can be used in the Hölder global optimization, as well. Convergence condition are given. Numerical experiments show quite a promising performance of the new technique.

Space-filling curves and multiple estimates of Hölder constants in derivative-free global optimization

LERA, DANIELA;
2016-01-01

Abstract

In this paper the global optimization problem where the objective function is multiextremal and satisfying the Lipschitz condition over a hyperinterval is considered. An algorithm that uses Peano-type space-filling curves to reduce the original Lipschitz multi-dimensional problem to a univariate one satisfying the Hölder condition is proposed. The algorithm at each iteration applies a new geometric technique working with a number of possible Hölder constants chosen from a set of values varying from zero to infinity showing so that ideas introduced in a popular DIRECT method can be used in the Hölder global optimization, as well. Convergence condition are given. Numerical experiments show quite a promising performance of the new technique.
2016
9780735413924
Classes of test functions; Derivative-free global optimization; Deterministic numerical algorithms; DIRECT; Hölder functions; Lipschitz functions; Space-filling curves; Physics and astronomy (all)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/188043
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