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Determining solution set of nonlinear inequalities using space-filling curves for finding working spaces of planar robots

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Abstract

In this paper, the problem of approximating and visualizing the solution set of systems of nonlinear inequalities is considered. It is supposed that left-hand parts of the inequalities can be multiextremal and non-differentiable. Thus, traditional local methods using gradients cannot be applied in these circumstances. Problems of this kind arise in many scientific applications, in particular, in finding working spaces of robots where it is necessary to determine not one but all the solutions of the system of nonlinear inequalities. Global optimization algorithms can be taken as an inspiration for developing methods for solving this problem. In this article, two new methods using two different approximations of Peano–Hilbert space-filling curves actively used in global optimization are proposed. Convergence conditions of the new methods are established. Numerical experiments executed on problems regarding finding the working spaces of several robots show a promising performance of the new algorithms.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Cagliari, Cagliari, Italy

    Daniela Lera

  2. Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, Università della Calabria, Rende, Italy

    Maria Chiara Nasso

  3. Federal Research Center Computer Science and Control of Russian Academy of Sciences, Moscow, Russia

    Mikhail Posypkin

  4. Lobachevskiy State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Yaroslav D. Sergeyev

Authors
  1. Daniela Lera
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  2. Maria Chiara Nasso
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  3. Mikhail Posypkin
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  4. Yaroslav D. Sergeyev
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Correspondence to Yaroslav D. Sergeyev.

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Lera, D., Nasso, M.C., Posypkin, M. et al. Determining solution set of nonlinear inequalities using space-filling curves for finding working spaces of planar robots. J Glob Optim (2024). https://doi.org/10.1007/s10898-023-01352-2

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