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

Author

Listed:
  • Daniela Lera

    (Università di Cagliari)

  • Maria Chiara Nasso

    (Università della Calabria)

  • Mikhail Posypkin

    (Federal Research Center Computer Science and Control of Russian Academy of Sciences)

  • Yaroslav D. Sergeyev

    (Lobachevskiy State University of Nizhni Novgorod)

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.

Suggested Citation

  • Daniela Lera & Maria Chiara Nasso & Mikhail Posypkin & Yaroslav D. Sergeyev, 2024. "Determining solution set of nonlinear inequalities using space-filling curves for finding working spaces of planar robots," Journal of Global Optimization, Springer, vol. 89(2), pages 415-434, June.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:2:d:10.1007_s10898-023-01352-2
    DOI: 10.1007/s10898-023-01352-2
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    References listed on IDEAS

    as
    1. Yuri Evtushenko & Mikhail Posypkin & Larisa Rybak & Andrei Turkin, 2018. "Approximating a solution set of nonlinear inequalities," Journal of Global Optimization, Springer, vol. 71(1), pages 129-145, May.
    2. Lera, Daniela & Posypkin, Mikhail & Sergeyev, Yaroslav D., 2021. "Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    3. Antanas Žilinskas & Julius Žilinskas, 2013. "A hybrid global optimization algorithm for non-linear least squares regression," Journal of Global Optimization, Springer, vol. 56(2), pages 265-277, June.
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