Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics

Daniela Lera, Mikhail Posypkin and Yaroslav D. Sergeyev

Applied Mathematics and Computation, 2021, vol. 390, issue C

Abstract: The problem of approximating and visualizing the solution set of systems of nonlinear inequalities can be frequently met in practice, in particular, when it is required to find the working space of some robots. In this paper, a method using Peano-Hilbert space-filling curves for the dimensionality reduction has been proposed for functions satisfying the Lipschitz condition. Theoretical properties of the introduced algorithm showing advantages of this reduction in the context of the present problem have been established and convergence properties of this method have been studied. A number of experiments executed on test functions and problems regarding finding workspace of robots confirm theoretical results and show a promising character of the new methodology.

Keywords: Systems of nonlinear inequalities; Space-filling curves; Global optimization; Derivative-free methods; Robot workspace (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320305762

DOI: 10.1016/j.amc.2020.125660

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