In this paper, the Lipschitz global optimization problem is considered both in the cases of non-differentiable and differentiable objective functions over hyperintervals. It is shown that space-filling curves can be successfully used to extend promising one-dimensional methods to the multidimensional case. In particular, several DIRECT-based algorithms using Peano-Hilbert space-filling curves and adaptive diagonal curves are surveyed.
Possible Extensions to the DIRECT Global Optimization Algorithm Based on Space-Filling and Diagonal Curves
Daniela LeraSecondo
;
2023-01-01
Abstract
In this paper, the Lipschitz global optimization problem is considered both in the cases of non-differentiable and differentiable objective functions over hyperintervals. It is shown that space-filling curves can be successfully used to extend promising one-dimensional methods to the multidimensional case. In particular, several DIRECT-based algorithms using Peano-Hilbert space-filling curves and adaptive diagonal curves are surveyed.
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